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ANALYSIS OF $(f,g)$-DERIVATIONS IN PSEUDO NEAR SEMIRINGS
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This paper investigates $(f,g)$-derivations, a generalization of derivations, in pseudo near semirings $N$, where $f$ and $g$ are mappings from $N$ into itself. We examine the fundamental properties of these mappings and their interactions within the structure of pseudo near semirings. Furthermore, we prove that nth order $(f,g)$-derivations satisfy the Leibniz rule. Finally, we extend Posner’s first theorem to $(f,g)$-derivations in $N$.
Pushpa Publishing House
Title: ANALYSIS OF $(f,g)$-DERIVATIONS IN PSEUDO NEAR SEMIRINGS
Description:
This paper investigates $(f,g)$-derivations, a generalization of derivations, in pseudo near semirings $N$, where $f$ and $g$ are mappings from $N$ into itself.
We examine the fundamental properties of these mappings and their interactions within the structure of pseudo near semirings.
Furthermore, we prove that nth order $(f,g)$-derivations satisfy the Leibniz rule.
Finally, we extend Posner’s first theorem to $(f,g)$-derivations in $N$.
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