z-ideals in the Semiring ℛ^+(L_τ)

Abstract

Let ℛ^+(L_τ) denote the nonnegative τ-real-continuous function on a topoframe L_τ. We introduce the notion of z-ideals and maximal ideals in the semiring ℛ^+(L_τ) and state some results about them. Also, we show that the topoframe L_τ is a P-topoframe if and only if the semiring ℛ^+(L_τ) is a regular semiring.

Keywords

• z-congruence
• z-ideal
• topoframe
• τ-real-continuous function