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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 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.

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Authors and Affiliations

  1. Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran

    Peyman Nasehpour

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  1. Peyman Nasehpour
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Correspondence to Peyman Nasehpour.

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Dedicated to Professor Carlos Martín-Vide.

Presented by M. Jackson.

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Nasehpour, P. Pseudocomplementation and minimal prime ideals in semirings. Algebra Univers. 79, 11 (2018). https://doi.org/10.1007/s00012-018-0496-x

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  • DOI: https://doi.org/10.1007/s00012-018-0496-x

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