Algebra universalis

, 79:11 | Cite as

Pseudocomplementation and minimal prime ideals in semirings

Article

Abstract

In Section 2 of the present paper, we introduce the concept of pseudocomplementation for semirings and show the semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some interesting results for minimal prime ideals of such semirings. In Section 3, some classical results for minimal prime ideals in ring theory are generalized in the context of semiring theory.

Keywords

Semiring Bounded distributive lattice Minimal prime ideal Pseudocomplemented elements Stone elements Dense elements 

Mathematics Subject Classification

16Y60 06D15 13A15 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering ScienceGolpayegan University of TechnologyGolpayeganIran

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