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What is Abelian Group

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras
Commutative group.
Published in Chapter:
Theoretical Study of the NeutroAlgebra Generated by the Combining Function in Prospector and Some Pedagogical Notes
Noel Batista Hernández (Asociación Latinoamericana de Ciencias Neutrosóficas, Ecuador), Erick González Caballero (Technological University of Havana, Cuba), Lilia Esther Valencia Cruzaty (Universidad Estatal Península de Santa Elena, Ecuador), Wilmer Ortega Chávez (Universidad Nacional Intercultural de la Amazonia, Peru), Carmen Flor Padilla Huarac (Universidad Nacional José Faustino Sánchez Carrión, Peru), and Selene Luz Chijchiapaza Chamorro (Universidad Nacional Daniel Alcides Carrión, Peru)
DOI: 10.4018/978-1-6684-3495-6.ch008
Abstract
NeutroAlgebras consist of algebras containing at least one NeutroAxiom. In the literature, there is a method for decision-making in a migrational situation that uses a NeutroAlgebra generated by the combining function in Prospector. This method is an important hit in showing both the utility and theoretical significance of NeutroAlgebras since it uses this abstract tool for solving a real-life problem. To the authors' knowledge, this is the only approach to NeutroAlgebras which is not exclusively theoretical. This chapter presents the rigorous mathematical proofs of the properties of that NeutroAlgebra because so far the theoretical approaches to the proposed method are minimal. The deeper mathematical knowledge of this specific NeutroAlgebra is a contribution to the general theory on this subject. The authors expect that this chapter will serve as dissemination of NeutroAlgebras among undergraduate and graduate students who may be interested in this issue.
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Sustainability of Public Key Cryptosystem in Quantum Computing Paradigm
An Abelian group is a group for which the elements commute (i.e., AB = BA for all elements A and B ). Abelian groups therefore correspond to groups with symmetric multiplication tables.
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