Selected Works of MAURICE AUSLANDER

Selected Works of MAURICE AUSLANDER, Part 1
	Front Matter
		MAURICE AUSLANDER -- August 3, 1926-November 18, 1994 (Photograph courtesy of Gordana Todorov.)
		Contents
		Foreword
		Maurice Auslander 1926-1994
		Curriculum Vitae
		Publication list for Maurice Auslander
	Chapter I. Homological dimension and local rings
		[1] On the dimension of modules and algebras (III), Global dimension, Nagoya Math. J. 9 (1955) 67-77.
		[2] (with R. C. Lyndon) Commutator subgroups of free groups, Amer. J. Math. 77 (1955) 929-931.
		[4] On the dimension of modules and algebras (VI), Comparison of global and algebra dimension, Nagoya Math. J. 11 (1957) 61-65.
		[5] On regular group rings, Proc. Amer. Math. Soc. 8 (1957) 658-665.
		[6] (with D. Buchsbaum) Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957) 390-405.
		[7] (with D. Buchsbaum) Homological dimension in noetherian rings II, Trans. Amer. Math. Soc. 88 (1958) 194-206.
		[10] (with D. Buchsbaum) Codimension and multiplicity, Ann. of Math. 68 (1958) 625-657. Correction, Ann. of Math. (2) 70 (1959) 395-397.
		[12] (with D. Buchsbaum) Unique factorization in regular local rings, Proc. Nat. Acad. Sci. USA 45 (1959) 733-734.
		[19] A remark on a paper of M. Hironaka, Amer. J. Math. 84 (1962} 8-10.
	Chapter II. Ramification theory
		[13] (with D. Buchsbaum) On ramification theory in noetherian rings, Amer. J. Math. 81 (1959) 749-765.
		[14] (with O. Goldman) Maximal orders, Trans. Amer. Math. Soc. 97 (1960) 1-24.
		[15] (with O. Goldman) The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960) 367-409.
		[16] Modules over unramified regular local rings, Illinois J. Math. 5 (1961) 631-647.
		[18] On the purity of the branch locus, Amer. J. Math. 84 (1962) 116-125.
		[20] (with D. S. Rim) Ramification index and multiplicity, Illinois J. Math. 7 (1963) 566-581.
		[21] Modules over unramified regular local rings, Proc. International Congr. Mathematicians, Stockholm (1962) 230-233, Inst. Mittag-Leffler, Djursholm, 1963.
		[26] (with A. Brumer) Brauer groups of discrete valuation rings, Nederl. Akad. Wetensch. Proc. Ser. A, 71, no. 3 (1968) 286-296.
		[88] (with I. Reiten and S. O. Smalø) Galois actions on rings and finite Galois coverings, Math. Scand. 65 (1989) No. 1, 5-32.
	Chapter III. Functors
		[22] Coherent functors, Proc. Conf. Categorial Algebra (La Jolla, Calif. 1965) 189-231, Springer, New York, 1966.
		[31] (with I. Reiten) Stable equivalence of artin algebras, Proc. Conf. on Orders, Group rings and related topics (Ohio 1972) 8-71, Lecture Notes in Math. 353, Springer, Berlin 1973.
		[35] (with I. Reiten) Stable equivalence of dualizing R-varieties, Adv. in Math. 12 (1974) No. 3, 306-366.
		[67] A functorial approach to representation theory, Representations of algebras. (ICRA III, Puebla 1980) 105-179. Lecture Notes in Math. 944, Springer, Berlin New York, 1982.
		[105] (with M. Kleiner) Adjoint functors and an extension of the Green correspondance for group representations, Adv. in Math. 104, (1994) No. 2, 297-314.
		[107] (with I. Reiten) D Tr-periodic modules and functors, Representation theory of algebras (ICRA VII, Cocoyoc 1994) 39-50, CMS Conf. Proc. 18, Amer. Math. Soc., Providence, RI, 1996.
	Chapter IV. Almost split sequences and artin algebras
		[28] Representation dimension of artin algebras, Queen Mary College, Mathematics Notes, University of London (1971).
		[29] (with K. W. Roggenkamp) A characterization of orders of finite lattice type, Invent. Math. 17 (1972) 79-84.
		[33] Representation theory of artin algebras I, Comm. Algebra 1 (1974) 177-268.
		[34] Representation theory of artin algebras II, Comm. in Algebra 1 (1974) 269-310.
		[36] (with I. Reiten) Representation theory of artin algebras III: Almost split sequences, Comm. Algebra 3 (1975) 239-294.
		[47] Large modules over artin algebras, Algebra, Topology and Category theory, (A collection of papers in honor of Samuel Eilenberg) 1-17 Academic Press, New York, 1976.
		[49] (with I. Reiten) Representation theory of artin algebras IV: Invariants given by almost split sequences, Comm. Algebra 5 (1977) 443-518.
		[50] (with I. Reiten) Representation theory of artin algebras V: Methods for computing almost split sequences and irreducible morphisms, Comm. Algebra 5 (1977) No. 5, 519-554.
		[52] (with I. Reiten) Representation theory of artin algebras VI: A functorial approach to almost split sequences, Comm. Algebra 6 (1978) No. 3, 257-300.
		[54] (with M. I. Platzeck) Representation theory of hereditary artin algebras, Representation theory of algebras, (Proc. Conf. Temple Univ., 1976) 389-424. Lecture Notes in Pure Appl. Math. 37, Dekker, New York, 1978.
		[58] (with R. Bautista, M. I. Platzeck, I. Reiten and S. O. Smalø) Almost split sequences whose middle term has at most two indecomposable summands, Canad. J. Math. 31, (1979) No 5, 942-960.
		[68] Relations for Grothendieck groups of artin algebras, Proc. Amer. Math. Soc. 91 (1984) No. 3, 336-340.
	Chapter V. Some topics in representation theory
		[41] (with I. Reiten) On a generalized version of the Nakayama conjecture, Proc. Amer. Math. Soc. 52 (1975) 69-74.
		[45] (with E. L. Green and I. Reiten) Modules with waists, Illinois J. Math. 19 (1975) 467-477.
		[69] (with I. Reiten) Modules determined by their composition factors, Illinois J. Math. 29 (1985) No. 2, 280-301.
		[72] (with J. F. Carlson) Almost-split sequences and group rings, J. Algebra 103 (1986) No. 1, 122-140.
		[94] (with I. Reiten) On a theorem of E. Green on the dual of the transpose, Representations of finite-dimensional algebras (Tsukuba 1990) 53-65, CMS Conf. Proc., 11, Amer. Math. Soc., Providence RI (1991) 53-65.
	Acknowledgments
Selected Works of MAURICE AUSLANDER, Part 2
	Front Matter
		MAURICE AUSLANDER -- August 3, 1926-November 18, 1994 (Photograph courtesy of Gordana Todorov.)
		Contents
		Foreword
		Publication list for Maurice Auslander
	Chapter VI. Lattices over general orders
		[55] Functors and morphisms determined by objects, Representation theory of algebras (Proc. Conf. Temple Univ., 1976), 1-244. Lecture Notes in Pure Appl. Math. 37, Dekker, New York 1978.
		[56] Applications of morphisms determined by modules, Representation theory of algebras (Proc. Conf. Temple Univ. 1976), 245-327. Lecture Notes in Pure Appl. Math. 37, Dekker, New York 1978.
		[76] A survey of existence theorems for almost split sequences, Representations of algebras (Durham, 1985), 81-89, London Math. Soc. Lecture Note Ser. 116, Cambridge Univ. Press, Cambridge-New York, 1986.
	Chapter VII. Tilting theory and homologically finite subcategories
		[57] (with M. I. Platzeck and I. Reiten) Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979) 1-46.
		[62] (with S. O. Smalø) Preprojective modules over artin algebras, J. Algebra 66, (1980) No. 1, 61-122.
		[63] (with S. O. Smalø) Almost split sequences in subcategories, J. Algebra 69, (1981) No. 2, 426-454, with Addendum J. Algebra, 71 (1981) No. 2 ,592-594.
		[92] (with I. Reiten) Applications of contravariantly finite subcategories, Adv. in Math. 86, No. 1 (1991) 111-152.
		[96] (with M. I. Platzeck and G. Todorov) Homological theory of idempotent ideals, Trans. Amer. Math. Soc. 332 (1992) No. 2, 667-692.
	Chapter VIII. Almost split sequences and commutative rings
		[71] Isolated singularities and existence of almost split sequences, Representation theory II (ICRA IV, Ottawa, 1984) 194-241, Lecture Notes in Math. 1178, Springer, Berlin-New York, 1986.
		[74] Rational singularties and almost split sequences, Trans. Amer. Math. Soc. 293 (1986) No. 2, 511-531.
		[78] (with I. Reiten) Almost split sequences for rational double points, Trans. Amer. Math. Soc. 302 (1987) No. 1, 87-97.
		[79] (with I. Reiten) The Cohen-Macaulay type of Cohen-Macaulay rings, Adv. in Math., 73 (1989), No. 1, 1-23.
		[83] (with I. Reiten) Almost split sequences for Cohen-Macaulay modules, Math. Ann. 277 (1987) No. 2, 345-349.
		[84] The what, where and why of almost split sequences, Proceedings of the International Congress of Mathematicians, vol. 1-2, (Berkeley, CA, 1986) 338-345, Amer. Math. Soc., Providence, RI, 1987.
		[85] (with I. Reiten) Cohen-Macaulay modules for graded Cohen-Macaulay rings and their completions, Commutative Algebra, (Berkeley, CA, 1987) 21-31, Math. Sci. Res. Inst. Publ. 15 Springer, Berlin-New York, 1989.
		[90] (with I. Reiten) Graded modules and their completions, Topics in Algebra, Part 1 (Warsaw 1989) 181-192, Banach Center Publ. 26, Part 1, PWN, Warsaw 1990.
	Chapter IX. Grothendieck groups and Cohen-Macaulay approximations
		[73] (with I. Reiten) Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39 (1986) No. 1-2, 1-51.
		[86] (with I. Reiten) Grothendieck groups of algebras with nilpotent annihilators, Proc. Amer. Math. Soc. 103 (1988), No. 4, 1022-1024.
		[89] (with R. O. Buchweitz) The homological theory of maximal Cohen-Macaulay approximations, Colloque en l'honneur de Pierre Samuel (Orsay 1987), Mém. Soc. Math. France, (N.S.) No. 38 (1989) 5-37.
		[97] (with S. Ding and Ø. Solberg) Liftings and weak liftings of modules, J. Algebra 156 (1993) No. 2, 273-317.
	Chapter X. Relative theory and syzygy modules
		[98] (with Ø. Solberg) Relative homology and representation theory I, Relative homology and homologically finite subcategories, Comm. Algebra 21 (9) (1993) 2995-3031.
		[99] (with Ø. Solberg) Relative homology and representation theory II, Relative cotilting theory, Comm. Algebra 21 (9) (1993) 3033-3079.
		[102] (with I. Reiten) k-Gorenstein algebras and syzygy modules, J. Pure Appl. Algebra 92 (1994) 1-27.
		[108] (with I. Reiten) Syzygy modules for noetherian rings, J. Algebra 183 (1996) No. 1, 167-185.
	Acknowledgments
Not Selected Works of Maurice Auslander
	[3] (with D. Buchsbaum) Homological dimension in noetherian rings, Proc. Nat. Acac. Sci. 42 (1956) 36-38.
	[8] (with L. Auslander) Solvable Lie groups and locally Euclidean Riemann spaces, Proc. Amer. Math. Soc. 9 (1958) 933-941.
	[9] (with A. Rosenberg) Dimension of ideals in polynomial rings, Can. J. Math. 10 (1958) 287-293.
	[11] Remark on automorphisms of groups, Proc. Amer. Math. Soc. 9 (1958) 229-230.
	[17] (with D. Buchsbaum) Invariant factors and two criteria for projectivity of modules, Trans. Amer. Math. Soc. 104 (1962) 516-522.
	[23] Remarks on a theorem of Bourbaki, Nagoya Math. J. 27 (1966) 361-369.
	[25] Comments on the functor Ext^1(C, ), Topology 8 (1969) 151-166.
	[37] (with I. Reiten) Stable equivalence of dualizing R-varieties II Hereditary dualizing R-varieties, Adv. in Math. 17, (1975) No. 2, 93-121.
	[38] (with I. Reiten) Stable equivalence of dualizing R-varieties III Dualizing R-varieties stably equivalent to hereditary dualizing R-varieties, Adv. in Math. 17 (1975) No. 2, 122-142.
	[39] (with I. Reiten) Stable equivalence of dualizing R-varieties IV Higher global dimension, Adv. in Math. 17, (1975) No. 2, 143-166.
	[40] (with I. Reiten) Stable equivalence of dualizing R-varieties V Artin algebras stably equivalent to hereditary algebras, Adv. in Math. 17, (1975) No. 2, 167-195.
	[40.1] Idun Reiten, Stable equivalence of dualizing R-varieties VI. Nakayama Dualizing R-Varieties, Adv. in Math. 17, (1975) No. 2, 196-211.
	[42] Almost split sequences I, Proc. Int. Conf. on representations of algebras, Ottawa 1974, Lecture Notes in Math. 488 Springer-Verlag (1975) 1-8.
	[43] (with I. Reiten) Almost split sequences II, Proc. Int. Conf. on representations of algebras, Carleton Univ., (Ottawa 1974), Lecture Notes in Math. 488, Springer Verlag (1975) 9-19.
	[44] (with E. L. Green and I. Reiten) Modules having waists, Proc. Int. Conf. on representations of algebras, Ottawa 1974, Lecture Notes in Math. 488, Springer Verlag (1975) 20-28.
	[48] (with I. Reiten) On the representation type of triangular matrix rings, J. London Math. Soc. (2), 12 (1976) No. 3, 371-382.
	[53] (with M. I. Platzeck and I. Reiten) Periodic modules over weakly symmetric algebras, J. Pure Appl. Algebra 11 (1977) 279-291.
	[60] (with S. O. Smalø) Preprojective modules An introduction and some applications, Representation theory II (Proc. ICRA II, Carleton Univ., Ottawa 1979) 48-73. Lecture Notes in Math. 832, Springer, Berlin, 1980.
	[61] (with I. Reiten) Uniserial functors, Representation theory II (Proc. ICRA II, Carleton Univ., Ottawa 1979) 1-47, Lecture Notes in Math. 832, Springer, Berlin, 1980.
	[64] (with S. O. Smalø) Preprojective lattices over classical orders. Integral representations and applications. (Oberwolfach 1980) 326-345. Lecture Notes in Math. 882, Springer, Berlin-New York 1981.
	[65] Representation theory of finite-dimensional algebras, Algebraists' homage papers in ring theory and related topics (New Haven, Conn,. 1981), 27-39, Contemp. Math. 13, Amer. Math. Soc., Providence, R.I., 1982.
	[66] (with S. O. Smalø) Lattices over orders Finitely presented functors and preprojective partitions, Trans. Amer. Math. Soc. 273 (1982) No. 2, 433-445.
	[70] Finite type implies isolated singularity, Orders and their applications (Oberwolfach, 1984), 1-4, Lecture Notes in Math. 1142, Springer, Berlin-New York, 1985.
	[75] (with I. Reiten) McKay quivers and extended Dynkin diagrams, Trans. Amer. Math. Soc. 293 (1986) No. 1, 293-301.
	[77] Almost split sequences and algebraic geometry, Representations of algebras (Durham, 1985), 165-179, London Math. Soc. Lecture Note Ser. 116, Cambridge Univ. Press, Cambridge-New York, 1986.
	[80] (with I. Reiten) Almost split sequences in dimension two, Adv. in Math. 66 (1987) No. 1, 88-118.
	[81] (with I. Reiten) Almost split sequences for Z-graded rings, Singularities, representation of algebras and vector bundles (Lambrecht 1985), 232-243, Lecture Notes in Math. 1273, Springer, Berlin-New York(1987).
	[82] (with I. Reiten) Almost split sequences for abelian group graded rings, J. Algebra, 114 (1988) No. 1, 29-39.
	[91] (with E. L. Green) Modules over endomorphism rings, Comm. Algebra 20 (5) (1992) 1259-1278.
	[93] (with I. Reiten) Cohen-Macaulay and Gorenstein artin algebras, Representation theory of finite groups and finite-dimensional algebras, (Bielefeld 1991) 221-245, Progr. Math. 95, Birkhauser, Basel (1991).
	[95] (with I. Reiten) Homologically finite subcategories, Representations of algebras and related topics (ICRA V, Tsukuba 1990). London Math. Soc. Lecture Note Ser. 168, 1-42 (199).
	[100] (with Ø. Solberg) Relative homology and representation theory III, Cotilting modules and Wedderburn correspondence, Comm. Algebra 21 (9) (1993) 3081-3097.
	[101] (with Ø. Solberg) Gorenstein algebras and algebras with dominant dimension at least 2, Comm. Algebra 21 (11) (1993) 3897-3934.
	[103] (with M. Kleiner) The Green correspondence for adjoint functors, Representations of algebras (ICRA VI, Ottawa 1992) 69-81, CMS Conf. Proc. 14, Amer. Math. Soc., Providence, RI, 1993.
	[104] (with Ø. Solberg) Relative homology, Finite-dimensional algebras and related topics (ICRA VI, Ottawa 1992) Kluwer Academic Publishers, Nato Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424 (1994) 347-359.