Abstract

AbstractIn this paper, we consider the composition of derivations in Boolean semirings and investigate the conditions that the composition of two derivations is a derivation. We also show that the nth derivation of a derivation d, denoted by dn, on a Boolean semiring satisfies Leibniz rule. Finally, we show that any locally nipotent derivations on a zero-symmetric Boolean semiring must be zero.

Highlights

  • The notion of the ring with derivation plays a significant role in the integration of analysis, algebraic geometry and algebra

  • Posner considered the composition of derivations and showed that the composition of two nonzero derivations of a prime ring R cannot be a derivation provided that characteristic of R is different from 2

  • The objective of this paper is to study the composition of derivations on Boolean semiring

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Summary

Introduction

The notion of the ring with derivation plays a significant role in the integration of analysis, algebraic geometry and algebra. By a derivation of a ring R, we mean any function d:R → R which satisfies the following conditions: (i) d(a + b) = d(a) + d(b) and (ii) d(ab) = d(a)b + ad(b), for all a, b ∈ R. Her research interests are Ring Theory (derivations, commutativity conditions in rings), Universal algebra and Combinatorics. The objective of this paper is to study the composition of derivations on Boolean semiring.

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