Complemented Semiring Satisfying the Identity u + 1 = 1 + u = u

Authors

  • Chandrakala H.K Department of Mathematics, Bangalore Institute of Technology, K.R Road, V.V Pura, Bangalore-04, India.
  • A. Rajeswari Department of Mathematics, Bangalore Institute of Technology, K.R Road, V.V Pura, Bangalore-04, India.

DOI:

https://doi.org/10.9734/bpi/mono/978-93-49238-47-3/CH6

Keywords:

Complemented semiring, quasi-separative, weakly separative, rectangular band, idempotent

Abstract

This paper contains some results on complemented semirings involving one variable. We consider complemented semiring (S1, +, .) satisfying the identity u + 1=1 + u = u for all u, v in S1 then it is proved that (S1, +) is quasi, weakly, separative and also (S1, +, .) is an idempotent. For this complemented semiring we also determine the additive and multiplicative structures. Complemented semiring is holds and equivalent many results by using the identity u + 1 = 1 + u = u for all u, v in S1.

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Published

2025-02-10

How to Cite

Chandrakala H.K, & A. Rajeswari. (2025). Complemented Semiring Satisfying the Identity u + 1 = 1 + u = u. Innovative Solutions: A Systematic Approach Towards Sustainable Future, Edition 1, 50–58. https://doi.org/10.9734/bpi/mono/978-93-49238-47-3/CH6

Issue

Innovative Solutions: A Systematic Approach Towards Sustainable Future, Edition 1

Section

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