Factorization of elements in noncommutative rings, I
We extend the classical theory of factorization in noncommutative integral domains to the more general classes of right saturated rings and right cyclically complete rings. Our attention is focused, in particular, on the factorizations of right regular elements into left irreducible elements. We stu...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/160 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543296304709632 |
|---|---|
| author | Facchini, Alberto Fassina, Martino |
| author_facet | Facchini, Alberto Fassina, Martino |
| author_sort | Facchini, Alberto |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-12-30T22:42:45Z |
| description | We extend the classical theory of factorization in noncommutative integral domains to the more general classes of right saturated rings and right cyclically complete rings. Our attention is focused, in particular, on the factorizations of right regular elements into left irreducible elements. We study the connections among such factorizations, right similar elements, cyclically presented modules of Euler characteristic $0$ and their series of submodules. Finally, we consider factorizations as a product of idempotents. |
| first_indexed | 2025-12-02T15:25:41Z |
| format | Article |
| id | admjournalluguniveduua-article-160 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:25:41Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-1602016-12-30T22:42:45Z Factorization of elements in noncommutative rings, I Facchini, Alberto Fassina, Martino Divisibility; Factorization; Right irreducible element 16U30; 16B99 We extend the classical theory of factorization in noncommutative integral domains to the more general classes of right saturated rings and right cyclically complete rings. Our attention is focused, in particular, on the factorizations of right regular elements into left irreducible elements. We study the connections among such factorizations, right similar elements, cyclically presented modules of Euler characteristic $0$ and their series of submodules. Finally, we consider factorizations as a product of idempotents. Lugansk National Taras Shevchenko University Universit\`a di Padova Fondazione Cassa di Risparmio di Padova e Rovigo 2016-12-31 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/160 Algebra and Discrete Mathematics; Vol 22, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/160/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
| spellingShingle | Divisibility Factorization Right irreducible element 16U30 16B99 Facchini, Alberto Fassina, Martino Factorization of elements in noncommutative rings, I |
| title | Factorization of elements in noncommutative rings, I |
| title_full | Factorization of elements in noncommutative rings, I |
| title_fullStr | Factorization of elements in noncommutative rings, I |
| title_full_unstemmed | Factorization of elements in noncommutative rings, I |
| title_short | Factorization of elements in noncommutative rings, I |
| title_sort | factorization of elements in noncommutative rings, i |
| topic | Divisibility Factorization Right irreducible element 16U30 16B99 |
| topic_facet | Divisibility Factorization Right irreducible element 16U30 16B99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/160 |
| work_keys_str_mv | AT facchinialberto factorizationofelementsinnoncommutativeringsi AT fassinamartino factorizationofelementsinnoncommutativeringsi |