Ideals of an EMV-semiring

In this paper, congruences, ideals, and prime ideals of an EMV-semiring and of its associated EMV-algebra are studied. Then EMV-semirings are characterized and it is proved that each EMV-semiring can be embedded into a direct product of a family of MV-semirings as an EMV-semiring. Moreover, another...

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Bibliographic Details
Published inInternational journal of general systems Vol. 49; no. 3; pp. 235 - 260
Main Authors Borzooei, R. A., Shenavaei, M., Di Nola, A., Zahiri, O.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.04.2020
Taylor & Francis LLC
Subjects
Algebra
Congruences
EMV-algebra
EMV-semiring
ideal
MV-algebra
MV-semiring
prime ideal
Representations
Rings (mathematics)
sheaf representation
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Summary:In this paper, congruences, ideals, and prime ideals of an EMV-semiring and of its associated EMV-algebra are studied. Then EMV-semirings are characterized and it is proved that each EMV-semiring can be embedded into a direct product of a family of MV-semirings as an EMV-semiring. Moreover, another representation of EMV-semirings are presented by EMV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of EMV-semirings over prime ideals. Also, using the categorical equivalence between EMV-semirings and EMV-algebras, a representation of EMV-algebras are obtained.
ISSN:0308-1079
1563-5104
DOI:10.1080/03081079.2020.1732368