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Pseudocomplementation and minimal prime ideals in semirings

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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… Click to show full 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: ideals semirings; theory; pseudocomplementation minimal; prime ideals; minimal prime

Journal Title: Algebra universalis
Year Published: 2018

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