Abstract
Objectives: The main objective of this article is to introduce *-Jordan ideals of a certain class of semirings called MA-semirings with involution and to investigate some conditions for which the above said ideals contained in the center. Methods and findings: We use the Jacobian identities and 2-torsion freeness of MA semirings. In this connection, we establish some important results of ring theory for the class of MA-semirings. Applications/ improvements: The commutative property is helpful to study the theory of semirings with ease therefore we find some conditions to impose commutativity in semirings, which are indeed novel idea in the field of semirings. Furthermore, these conditions are used in a most generalized way that these conditions bring the *-Jordan ideals to the center, therefore, it would be the corollary of result that semiring is commutative. Keywords: Semirings, *-Semirings, MA-Semirings, *-Jordan Ideals, *-Prime Semirings, Involution Mathematics Subject Classifications (2010): 16Y60, 16W10
Highlights
Introduction and PreliminariesIn literature, usually a self-inverse antiautomorphism for a given algebraic system is referred as involution [1,2,3,4,5,6]
The notion of semirings was introduced by authors in Refs. [7,8] introduced the concept of inverse semirings in 1974
The main aim of this study is to generalize some fundamental results of *-prime rings proved in Refs. [11,12] and investigate the condition for which the *-Jordan ideal is contained in the center of an MA-semiring
Summary
Introduction and PreliminariesIn literature, usually a self-inverse antiautomorphism for a given algebraic system is referred as involution [1,2,3,4,5,6]. [9], ( ) ( ) Javed et al studied additive inverse semirings satisfying y x + x' = x + x' y,∀x, y ∈S The main aim of this study is to generalize some fundamental results of *-prime rings proved in Refs. The following is one of the examples of prime MA semiring which is not a ring.
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