Algebra and Related Topics with Applications: ICARTA-2019, Aligarh, India, December 17–19

Organization
Preface
Contents
About the Editors
*-1.5pc  Algebra
Characterization of b-generalized Derivations in Rings with Involution
	1 Introduction
	2 Results
	References
Jordan Generalized n-derivations of Unital Algebras Containing Idempotents
	1 Introduction
	2 Preliminaries
	3 Multiplicative Jordan Generalized n-derivation
	4 Applications
	References
Variational Analysis of Approximate Defective Eigenvalues
	1 Introduction
	2 Approximate Multiple Eigenvalues
	3 Approximate Defective Eigenvalues
	References
Structure of Prime Near Rings with Generalized Derivations
	1 Introduction
	2 Main Results
	References
w-FP-projective Modules and Dimensions
	1 Introduction
	2 W-FP-projective Modules
	3 The W-FP-projective Dimension of Modules and Rings
	References
Central Values of X-generalized Skew Derivations on Right Ideals in Prime Rings
	1 Introduction
	2 An Auxiliary Generalized Polynomial Identity
	3 The Case of Inner X-generalized Skew Derivations
	4 The Main Result for Prime Rings
	5 The Main Result
		5.1 The Proof of Theorem 3
	References
Commutative Polynomial Rings which are Principal Ideal Rings
	1 Introduction
	2 Structure Theorem of PIRs
	3 Characterization of Polynomial Rings that Are PIRs
	4 Non-principal Ideals in Some Polynomial Rings
	References
Two Remarks on Generalized Skew Derivations in Prime Rings
	1 Annihilating Condition for a Single Generalized Skew Derivation
	2 Annihilating Conditions for Two Generalized Skew Derivations
	References
Dimensional Dual Hyperovals—An Updated Survey
	1 Introduction
		1.1 The Definition
		1.2 Basic Notions
	2 DHOs over mathbbFq, q>2
		2.1 Odd Characteristic
		2.2 Even Characteristic
	3 Split DHOs and DHO Sets
	4 DHOs with Ambient Spaces of Maximal Rank
		4.1 Yoshiara's Upper Bound for the Rank of an Ambient Space
		4.2 DHOs Meeting Yoshiara's (Conjectured) Bound for the Rank of an Ambient Space
		4.3 calVn(q), calHn, calDn and calTn Are Split
		4.4 Bilinear DHOs Whose Ambient Space Has Maximal Rank
	5 Quotients of DHOs
		5.1 Universal Covers
		5.2 Quotients of the Veronesean DHOs
		5.3 Quotients of the Huybrechts DHOs
		5.4 Quotients of the Buratti–Del Fra DHOs
		5.5 Quotients of the Taniguchi DHOs
	6 Duality
		6.1 Doubly Dual Hyperovals
		6.2 DHOs in Polar Spaces
		6.3 Knuth Operations
	7 Secondary Constructions
		7.1 Quotients of Spreads
		7.2 Quotients of Orthogonal Spreads
		7.3 Extensions of Bilinear DHOs
	8 Direct Constructions
		8.1 DHOs of Type calSc
		8.2 DHOs Constructed with Presemifields
	9 DHOs and Groups
		9.1 DHOs with Many Translation Groups
		9.2 DHOs with Many Extension Groups
		9.3 Doubly Transitive DHOs
	10 Miscellaneous Topics
		10.1 Edel's Characterization of Alternating DHOs
		10.2 Small DHOs over mathbbF2
	References
A Note on FMS Modules and FCP Extensions
	1 Introduction
	2 Results
	References
A Pair of Derivations of Prime Rings with Involution
	1 Some Preliminaries
	2 Main Results
	References
Basic One-Sided Ideals of Leavitt Path Algebras over Commutative Rings
	1 Introduction
	2 Preliminaries and Notation
	3 Basic One-Sided Ideals
	4 Minimal Basic Left Ideals Generated by a Vertex
	References
On Certain *-differential Identities in Prime Rings with Involution
	1 Introduction
	2 The Main Results
	References
On b-Generalized Derivations in Prime Rings
	1 Introduction and Notations
	2 The Results
	References
Commutativity of ast-Prime Rings with Generalized Derivations on ast-Jordan Ideals
	1 Introduction
	2 Auxiliary Lemmas
	3 Main Results
	4 Examples
	References
Local Subsemigroups and Variants of Some Classes of Semigroups
	1 Preliminaries
	2 Local Subsemigroups and Variants of Full Transformation Semigroups
	3 Variants of Symmetric Inverse Monoids
	4 Local Subsemigroups and Variants of Symmetric Inverse Monoids
	References
Closed Weak Supplemented Lattices
	1 Introduction
	2 Preliminaries
	3 Closed Weak Supplemented Lattices
	References
On Compatible Ring Structures of the Injective Hull of a Ring
	1 Introduction
	2 Essential Overrings Versus Rings of Quotients
	3 More on Compatible Ring Structures of E(RR)
	References
On Commutators Involving Derivations and Automorphisms in Prime Rings
	1 Motivation
	2 Preliminaries and Results
	References
Modules Invariant Under Clean Endomorphisms of Their Injective Hulls
	1 Introduction
	2 Clean-Invariant Modules
	References
A Note on Central Idempotents in Finite Group Rings of Symmetric Groups
	1 Introduction
	2 Proof (Theorem 1)
	References
Jordan Product Preserving Generalized Skew Derivations on Lie Ideals
	1 Introduction
	2 Inner Generalized Skew Derivations
		2.1 Proof of Proposition 2
	3 The Proof of Theorem 1
		3.1 Proof of Theorem 1
	References
Prime Rings with Generalized Derivations and Power Values on Lie Ideals
	1 Introduction
	2 Preliminary Results
	3 When mathscrT Is Generalized Inner Derivations
	4  The Study of General Case
	References
*-1.5pc  Coding Theory
On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes
	1 Introduction
	2 Reed-Muller Codes
	3 Characterizations of Purity
	References
Skew Constacyclic Codes over Fq+vFq
	1 Introduction
	2 Preliminaries
	3 Gray Map and Linear Codes over R
	4 v-Skew Constacyclic Codes over R
	5 Applications
	6 Conclusion
	References
Cyclic and LCD Codes over a Finite Commutative Semi-local Ring
	1 Introduction
	2 Basic Facts and Gray Map
	3 Linear Codes over mathfrakR
	4 Cyclic Codes over mathfrakR
	5 LCD Codes over mathfrakR
	6 Conclusion
	References
*-1.5pc  Graph Theory
Some Recent Results on the Graphs of Finite-Dimensional Vector Spaces
	1 Definitions and Preliminaries
	2 Introduction
	3 Non-zero Component Graphs on Finite-Dimensional Vector Spaces
	4 Non-zero Component Union Graph of a Finite-Dimensional Vector Space
	5 Distinct Component Graph on Finite-Dimensional Vector Space
	6 Component Intersection Graphs on Finite-Dimensional Vector Spaces
	7 Subspace Inclusion Graph mathcalIn(mathbbV)
	References
Two Value Graph Magma Algebras and Amenability
	1 Introduction
	2 Preliminaries
	3 Two Value Graph Magma Algebras
	4 Commutative Two Value Graph Magmas
	5 Amenable Bases for Commutative Two Value Graph Magma Algebras
	6 Further Results on Commutative Two Value Graph Magma Algebras
	References
Graph of Linear Transformations Over mathbbR
	1 Introduction
	2 Results
	References
On Distance Laplacian (Signless) Eigenvalues of Commuting Graphs of Dihedral and Dicyclic Groups
	1 Introduction
	2 Distance Laplacian Spectra of the Commuting Graphs of  D2n  and  Q4n
	3 Distance Signless Laplacian Spectra of the Commuting Graphs of  D2n  and  Q4n
	References
Spectrum of Graphs over Rings:  A Survey
	1 Introduction
	2 Spectrum of Graphs Associated to Rings
		2.1 Zero-Divisor Graphs
	3 Laplacian Spectrum of Graphs Associated to Rings
		3.1 Unitary Cayley Graphs
		3.2 Unit Graphs and Total Graphs
	References
On a New Extension of Annihilating-Ideal Graph of Commutative Rings
	1 Introduction
	2 Connectedness of Extended Sum Annihilating-Ideal Graph
	3 Extended Sum Annihilating-Ideal Graph as Some Special Type of Graphs
	4 Genus of Extended Sum Annihilating-Ideal Graph
	References
Spectrum of the 3-zero-divisor Hypergraph of Some Classes of Local Rings
	1 Introduction
	2 Adjacency Matrix of mathcalH3(mathbbZpn)
	3 Spectrum of mathcalH3(R)
	4 Laplacian Spectrum of mathcalH3(R)
	References
Complement of the Generalized Total Graph of Commutative Rings – A Survey
	1 Introduction
	2 Additive Graphs from Commutative Rings
	3 Generalized Total Graphs
	4 Complement of the Generalized Total Graph
	5 Complement of the Generalized Total Graph of mathbbZn
	6 Domination Properties of overlineGTP(mathbbZn)
	7 Complement of the Generalized Total Graph of Fields
	References