Rings, Monoids and Module Theory: AUS-ICMS 2020, Sharjah, United Arab Emirates, February 6–9 (Springer Proceedings in Mathematics & Statistics, 382)

Preface
Students of Daniel D. Anderson
Contents
About the Editors
Dan Anderson and His Mathematics
	References
Bounded and Finite Factorization Domains
	1 Introduction
	2 Preliminary
		2.1 General Notation
		2.2 Factorizations
	3 Bounded and Finite Factorization Monoids
		3.1 The Bounded Factorization Property
		3.2 The Finite Factorization Property
	4 Bounded and Finite Factorization Domains
		4.1 Characterizations of BFDs and (Strong) FFDs
		4.2 Some Relevant Classes of BFDs and FFDs
		4.3 The D+M Construction
	5 Subrings, Ring Extensions, and Localizations
		5.1 Inert Extensions
		5.2 Subrings
		5.3 Ring Extensions and Overrings
		5.4 Pullback Constructions
	6 Polynomial-Like Rings
		6.1 Bounded Factorization Subdomains of R[X] and R[[X]]
		6.2 Finite Factorization Subdomains of R[X] and R[[X]]
		6.3 Monoid Domains
		6.4 Graded Integral Domains
	7 Generalized Bounded and Finite Factorization Domains
	References
Factorization and Irreducibility in Modules
	1 Introduction
	2 Notions of Irreducibility
	3 Notions of Atomicity
	References
On -potent Domains and -homogeneous Ideals
	1 Introduction
		1.1 Introduction to Star Operations
	2 -homogeneous Ideals
	3 What -homogeneous Ideals Can Do
		3.1 -f-potent Domains
	References
On the Set of Molecules of Numerical and Puiseux Monoids
	1 Introduction
	2 Preliminary
	3 Molecules of Interval Numerical Monoids
	4 Molecularity of the Class of Numerical Monoids
		4.1 Atomic Classes of Puiseux Monoids
		4.2 A Conjecture on Molecularity
	5 Molecularity of Further Classes of Puiseux Monoids
		5.1 Molecularity of mathcalC2
		5.2 Molecularity of Non-Atomic Puiseux Monoids
	6 Infinite Molecularity
	References
Where Some Inert Minimal Ring Extensions of a Commutative Ring Come from, II
	1 Introduction
	2 Results
	3 Some Recent History and Some Open Questions
	References
A Survey on EM Conditions
	1 Introduction
	2 Annihilating Content
	3 EM-Rings
	4 The Noetherian Case
	5 Some Extensions of EM-Rings
	6 Some Generalizations
	References
Some Remarks on the D + M Construction
	References
On a Problem About Lowest Terms Domains Posed by D. D. Anderson
	1 Introduction
	2 Basic Properties of D
	3 Main Results
	References
Regularity and Related Properties in Tensor Products of Algebras Over a Field
	1 Introduction
	2 Preliminaries
	3 Tensor Products of Cohen–Macaulay k-Algebras
	4 Regularity, Gorensteiness, and Complete Intersection in Tensor Products
	5 Regularity of Tensor Products of Extension Fields and Applications
	References
Tame-Wild Dichotomy for Commutative Noetherian Rings—A Survey
	1 Introduction
	2 Tameness
		2.1 The Local Case
		2.2 Global Tameness
	3 A Dichotomy Theorem
	4 Wildness
	5 Non-wildness of Dedekind-Like Rings
		5.1 Brauer Groups
	6 What\'s Left?
		6.1 Field Extensions and Division Algebras
		6.2 Unsplit Dedekind-Like Rings
	References
On the Characterization of τ(n)-Atoms
	1 Introduction
	2 Preliminaries
	3 Structure of U\'(n)
	4 Tools for Determining τ(n)-irreducible Elements for U\'(n)
	5 Computational Results
	6 Conclusion
	References
Bounded Periodic Rings
	1 Introduction and Fundamentals
	2 The Main Results
	References
On Gracefully and Harmoniously Labeling Zero-Divisor Graphs
	1 Introduction
	2 Background
		2.1 Zero-Divisor Graphs
		2.2 Graceful Labeling
		2.3 Harmonious Labeling
	3 Labeling Results on Zero-Divisor Graphs of Commutative Rings
	4 Small Zero-Divisor Graphs
	References
A Survey on Genus of Selected Graphs from Commutative Rings
	1 Introduction
	2 Genus Properties of Graphs
	3 Zero-Divisor Graphs
	4 Jacobson Graphs
	5 Annihilator Graphs
	6 Unit Graphs
	7 Unitary Cayley Graphs and Cayley Sum Graphs
	8 Generalized Unit and Unitary Cayley Graphs
	References
A Computational Approach to Shephard Groups
	1 Introduction
	2 Preliminaries
		2.1 Gröbner-Shirshov Bases
		2.2 Complex Reflection Groups
	3 The Shephard Groups of Tetrahedral Type
		3.1 The Group G4
		3.2 The Group G5
		3.3 The Group G6
	4 The Shephard Groups of Octahedral Type
		4.1 The Group G8
		4.2 The Group G9
		4.3 The Group G10
		4.4 The Group G14
	5 The BMR Freeness Theorem for Hecke Algebras
	6 The BMM Symmetrizing Trace Conjecture
	References
BZS Near-Rings and Rings
	1 Introduction
	2 The BZS Property and Basic Results
	3 More Results on BZS Near-Rings and Rings
	4 Avenues for Future Work
	References