Complemented Semiring Satisfying the Identity u + 1 = 1 + u = u | Chapter 6 | Innovative Solutions: A Systematic Approach towards Sustainable Future

 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.

 

Author (s) Details

 

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.

 

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-49238-47-3/CH6