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Algebra, Abstract. --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory --- Àlgebra abstracta --- Àlgebres de Jordan --- Àlgebres de Lie --- Àlgebres no associatives --- Matrius (Matemàtica) --- Teoria dels reticles --- Lògica matemàtica

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This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.

Nonassociative algebras. --- Proof theory. --- Nonassociative rings. --- Algebra, Homological. --- Topological groups. --- Lie groups. --- Differential equations. --- Proof Theory and Constructive Mathematics. --- Non-associative Rings and Algebras. --- Category Theory, Homological Algebra. --- Topological Groups and Lie Groups. --- Differential Equations. --- Àlgebres no associatives

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Algebra, Abstract. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Àlgebra abstracta --- Àlgebres de Jordan --- Àlgebres de Lie --- Àlgebres no associatives --- Matrius (Matemàtica) --- Teoria dels reticles --- Lògica matemàtica

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Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Anells (Àlgebra) --- Monoides --- Mòduls (Àlgebra) --- Sistemes modulars (Àlgebra) --- Anells artinians --- Mòduls de Banach (Àlgebra) --- Mòduls de Cohen-Macaulay --- Mòduls injectius (Àlgebra) --- Mòduls projectius (Àlgebra) --- Teoria de divisors --- Teoria de torsió (Àlgebra) --- Grups finits --- Semigrups --- Anells algebraics --- Anells algèbrics --- Àlgebres no associatives --- Àlgebres topològiques --- Anells associatius --- Anells commutatius --- Anells de grup --- Anells no commutatius --- Ideals (Àlgebra) --- Representacions d'anells (Àlgebra) --- Teoria de la mesura

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This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory. One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.

Nonassociative rings. --- Functional analysis. --- Computer science—Mathematics. --- Coding theory. --- Information theory. --- Cryptography. --- Data encryption (Computer science). --- Data structures (Computer science). --- Non-associative Rings and Algebras. --- Functional Analysis. --- Mathematical Applications in Computer Science. --- Coding and Information Theory. --- Cryptology. --- Data Structures and Information Theory. --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Communication theory --- Communication --- Cybernetics --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Rings (Algebra) --- Àlgebres no associatives --- Data structures (Computer science)