Associative and Non-Associative Algebras and Applications: 3rd MAMAA, Chefchaouen, Morocco, April 12-14, 2018 (Springer Proceedings in Mathematics & Statistics)

Foreword
Preface
Acknowledgements
Contents
Contributors
*-20pt  Algebraic and Analytic Methods in Associative and Non-associative  Structures. Applications
Isomorphisms of Four Dimensional Perfect Non-simple Evolution Algebras
	1 Introduction
	2 The Maximal Basic Ideal Is One-Dimensional
		2.1 The Matrix U Has Two Zero Entries
		2.2 The Matrix U Has One Zero Entry
		2.3 The Matrix U Has No Nonzero Entries
	3 The Maximal Basic Ideal Is Two-Dimensional
		3.1 Take W=(1 0 0 1)
		3.2 Take W=(1 0 ω21 1)
		3.3 Take W=(1 ω12 ω21 1)
		3.4 Take W=(0 1 1 0)
	4 The Evolution Algebra Has a 3-Basic Ideal
		4.1 A Has a 3-Basic Ideal Which Has a 2-Basic Ideal
		4.2 No 3-Basic Ideal of A Has a 2-Basic Ideal
	References
Power-Associative Evolution Algebras
	1 Introduction
	2 Preliminaries
		2.1 Example of Jordan Algebra That Is Not Evolution Algebra
		2.2 Results About Nil Evolution Algebras
	3 Power Associativity
		3.1 Some Definitions
		3.2 Characterization of Associative Algebras
		3.3 Characterization of Power-Associative Algebras
		3.4 Characterization of Jordan Algebras
		3.5 Wedderburn Decomposition
	4 Classification
		4.1 Nil Indecomposable Associative Evolution Algebra
		4.2 Nil Indecomposable Evolution Algebra Which Is Not Associative
		4.3 General Classification
	References
A Survey on Isometries Between Lipschitz Spaces
	1 Introduction
	2 Scalar-Valued Linear Isometries
	3 Codimension 1 Linear Isometries
	4 Local Isometries
	5 Projections and Averages of Linear Isometries
	6 2-Local Isometries
	7 Vector-Valued Linear Isometries
	8 Scalar-Valued Hermitian Operators
	9 Vector-Valued Hermitian Operators
	10 Open Problems
	References
The Principal Eigenvalue for a Class of Singular Quasilinear Elliptic Operators and Applications
	1 Introduction
	2 Principal Eigenvalue
	3 Applications
		3.1 Existence of Solution
		3.2 Nonexistence of Solution to (Pλ)
		3.3 Uniqueness
		3.4 Bifurcation
		3.5 Homogenization
	References
Non-commutative Poisson Algebras Admitting a Multiplicative Basis
	1 Introduction and Previous Definitions
	2 Connections in the Set of Indexes. Decompositions
	3 The Minimal Components
	References
Multiplication Algebras: Algebraic and Analytic Aspects
	1 Introduction
	2 (Semi)prime Algebras
	3 Multiplicatively (Semi)prime Algebras
	4 An Interlude: A Multiplicative Non-associative Characterization of Integral Domains, and a Normed Variant
	5 Ultraprime Normed Algebras
	6 Totally Multiplicatively Prime Normed Algebras
	7 Complete Normed Algebras Whose Closed Multiplication Algebra Satisfies the von Neumann Inequality
	References
Generalized Drazin Inverse and Commuting Riesz Perturbations
	1 Introduction
	2 Riesz Perturbations of Generalized Drazin Invertibility
	3 Commuting Perturbation Class of Meromorphic Operators
	References
Generalized Rigid Modules and Their Polynomial Extensions
	1 Introduction
	2 Generalized Rigid Modules and Related Modules
	3 Triangular Matrix Modules and Polynomial Modules
	References
n-Ary k-Actions Between Sets and Their Applications
	1 Introduction and Previous Definitions
	2 Connections in mathfrakA Techniques
	3 Division Set Modules
	4 Arbitrary Graded k-Modules over Linear Spaces Induced by n-Linear Maps
	References
Primary Group Rings
	1 Primary Group Rings
	References
Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring
	1 Introduction
	2 Preliminaries
	3 Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring
	References
The 4-Rank of the Class Group of Some Real Pure Quartic Number Fields
	1 Introduction and Notations
	2 The 2 -Rank of  Cl(K)
	3 The 4-Rank of  Cl(K)
	4 Some Numerical Examples
	References
*-20pt  Homological and Categorical Methods in Algebra
Frobenius Monoidal Algebras and Related Topics
	1 Introduction
	2 Preliminaries
		2.1 Rigid Monoidal Categories
		2.2 Bimodule Categories
		2.3 Monads in 2-Categories
		2.4 Quasi-Hopf Algebras
	3 Frobenius (Monoidal) Algebras
		3.1 The Classical Case
		3.2 The Monoidal Case
		3.3 Frobenius Algebras in VectG
		3.4 Frobenius Algebras in Categories of Representations
		3.5 Frobenius Algebras in Categories of Corepresentations
	4 Frobenius Algebra Extensions and Frobenius (Monoidal) Functors
		4.1 Frobenius Algebra Extensions
		4.2 Hopf Galois Extensions
		4.3 Frobenius Functors and Frobenius Monads
		4.4 Frobenius Algebra Extensions in Monoidal Categories
		4.5 Monoidal Frobenius Functors
	5 Frobenius Wreaths and Cowreaths
		5.1 Frobenius Wreath Extensions
		5.2 Frobenius Functors for the Category of Generalized Entwined Modules
		5.3 Hopf Modules over Quasi-Hopf Algebras
	References
The Functor S-1C() and Its Relationship with Homological Functors T orn and overlineEXTn
	1 Introduction
	2 Definitions and Preliminary Results
	3 Functor S-1C(), Isomorphism and Adjoint Isomorphism
	4 The Action of SC-1() on the Homological Functors T orn and overlineEXTn
	References
BOCSES over Small Linear Categories and Corings
	1 Introduction
	2 The Monoidal Structure of the Category of Functors  on Small Categories
	3 BOCSES are Equivalent to Corings
	References
Quadratic Color Hom-Lie Algebras
	1 Introduction
	2 Quadratic Color Hom-Lie Algebras
	3 Constructions and Examples of Quadratic Color Hom-Lie Algebras
	4 Representations of Color Hom-Lie Algebras
	5 Extensions
		5.1 Elements of Cohomology
		5.2 Central Extensions
		5.3 T*-Extensions of Color Hom-Lie Algebras
	6 Color Hom-Leibniz Algebras Arising from Faulkner Construction
	References
The Extension Property in the Category of Direct Sum of Cyclic Torsion-Free Modules over a BFD
	1 Introduction
	2 The Extension Property in the Category CSp
	3 The Extension Property in the Category C0
		3.1 Preliminary and Notations
		3.2 Characterization of the Set En,p(Mn)
		3.3 Characterization of the Set Ep(M)
	References
*-20pt  History of Mathematics
Arabic Scientific and Technical Heritage in Morocco
	1 Introduction
	2 Mathematics
	3 Cryptography and Communication Systems
	4 Medicine
	5 Physics, Alchemy and Their Applications
	6 Other Disciplines
	7 Conclusions
	References