Invertible ideals and Gaussian semirings
| Autor: | Peyman Nasehpour, Shaban Ghalandarzadeh, Rafieh Razavi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics Gaussian 010102 general mathematics 0102 computer and information sciences Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences law.invention Semiring Valuation (logic) symbols.namesake Invertible matrix Section (category theory) 010201 computation theory & mathematics law FOS: Mathematics symbols 0101 mathematics Mathematics |
| Zdroj: | Archivum Mathematicum. :179-192 |
| ISSN: | 1212-5059 0044-8753 |
| DOI: | 10.5817/am2017-3-179 |
| Popis: | In the first section of this paper, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Pr\"{u}fer semirings and characterize them in terms of valuation semirings. In this section, we also characterize Pr\"{u}fer semirings in terms of some identities over its ideals such as $(I + J)(I \cap J) = IJ$ for all ideals $I$, $J$ of $S$. In the third section, we give a semiring version for the Gilmer-Tsang Theorem, which states that for a suitable family of semirings, the concepts of Pr\"{u}fer and Gaussian semirings are equivalent. At last we end this paper by giving a plenty of examples of proper Gaussian and Pr\"{u}fer semirings. Comment: Final version |
| Databáze: | OpenAIRE |
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