Posner’s theorems in semirings

S. Ganesh () and V. Selvan ()
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S. Ganesh: Ramakrishna Mission Vivekananda College (Autonomous)
V. Selvan: Ramakrishna Mission Vivekananda College (Autonomous)

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 597-602

Abstract: Abstract Various researchers extended and generalized the two main theorems of Posner [3] in multiple directions. In this paper we generalize these two main results to semirings. The main tool we use to accomplish this generalization is by defining derivation ( $$d^\Delta $$ d Δ ) in the ring of differences ( $$R^\Delta $$ R Δ ) of a semiring (R) corresponding to the derivation d of R.

Keywords: Semirings; Ring of differences; Derivations and Commutativity; 16N60; 16W25; 16Y60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00388-0

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