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

This proceedings is a collection of research papers on algebra and related topics, most of which were presented at the International Conference on Algebra and Related Topics with Applications (ICARTA-19), held at the Department of Mathematics, Aligarh Muslim University, Aligarh, India, from 17–19 December 2019. It covers a wide range of topics on ring theory, coding theory, cryptography, and graph theory. In addition to highlighting the latest research being done in algebra, the book also addresses the abundant topics of algebra particularly semigroups, groups, derivations in rings, rings and modules, group rings, matrix algebra, triangular algebra, polynomial rings and lattice theory. Apart from these topics, the book also discusses applications in cryptology, coding theory, and graph theory. 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