On certain identities of generalized derivations of semirings with involution
DOI:
https://doi.org/10.31489/2026m1/67-81Keywords:
semirings, MA-semirings, prime semirings, Hermitian elements, skew-Hermitian elements, involution, second kind involution, derivations, generalized derivationsAbstract
MA-semirings form a proper subclass of inverse semirings that properly contains both the class of rings and the class of distributive lattices with the least element. In this paper, we study generalized derivations satisfying certain algebraic identities of MA-semirings with involution. The main objective of this research is to investigate identities involving three, two, one generalized derivation in MA-semirings with involution, ensuring commutativity. Hermitian and skew-Hermitian elements are primarily used to formulate the basic tools for the development of this paper and these notions are the fundamental units of the second kind involution. Involution of the second kind plays a key role not only for proving the main results (see Theorems 1, 3, 5) but also it enables us to observe more results from their proofs (see Theorems 2, 4, 6). Since every derivation is a generalized derivation, the results obtained naturally extend a variety of results on derivations. Moreover, several well-established results on derivations of MA-semirings and rings under the similar environment can be concluded as special cases.
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