S-principal ideal multiplication modules
| Autor: | Emel Aslankarayiğit Uğurlu, Suat Koç, Ünsal Tekir |
|---|---|
| Přispěvatelé: | Aslankarayiğit Uğurlu E., Koç S., Tekir Ü. |
| Rok vydání: | 2023 |
| Předmět: |
Matematik
Commutative Rings and Algebras Multidisipliner Multidisciplinary Algebra and Number Theory MULTIDISCIPLINARY SCIENCES Logic Temel Bilimler Temel Bilimler (SCI) Doğa Bilimleri Genel Geometri ve Topoloji ÇOK DİSİPLİNLİ BİLİMLER MATHEMATICS NATURAL SCIENCES GENERAL Ayrık Matematik ve Kombinatorik Fizik Bilimleri Değişmeli Halkalar ve Cebirler MATEMATİK Natural Sciences (SCI) Physical Sciences Discrete Mathematics and Combinatorics Mantık Geometry and Topology Natural Sciences |
| Zdroj: | Communications in Algebra. 51:2510-2519 |
| ISSN: | 1532-4125 0092-7872 |
| Popis: | In this paper, we studyS-Principal ideal multiplication modules. LetA \" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">A A be a commutative ring with1≠0, S⊆A\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">1≠0, S⊆A1≠0, S⊆Aa multiplicatively closed set andM \" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">M M anA-module. A submoduleNofMis said to be anS-multipleofMif there exists∈S\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">s∈Ss∈Sand a principal idealIofAsuch thatsN⊆IM⊆N\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">sN⊆IM⊆NsN⊆IM⊆N.M \" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">M M is said to be anS-principal ideal multiplication moduleif every submoduleN \" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">N N ofM \" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">M M is anS-multiple ofM. Various examples and properties ofS-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extensionA⋉M\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">A⋉MA⋉Mis anS⋉0\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">S⋉0S⋉0-principal ideal ring. Also, we prove Cohen type theorem forS-principal ideal multiplication modules in terms ofS-prime submodules. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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