Generalization of primal superideals
Let R be a commutative super-ring with unity 16= 0. A proper super ideal of R is a super ideaI of R such that I 6=R.Letφ:I(R)→I(R)∪ {∅}be any function, where I(R) denotes the set of all proper super ideals of R. A homogeneous element a∈R is φ-prime to Iifra∈I−φ(I) whereris a homogeneous element in R...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155239 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Generalization of primal superideals / A. Jaber // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 202-213. — Бібліогр.: 13 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-155239 |
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Jaber, A. 2019-06-16T14:32:29Z 2019-06-16T14:32:29Z 2016 Generalization of primal superideals / A. Jaber // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 202-213. — Бібліогр.: 13 назв. — англ. 1726-3255 2010 MSC:13A02, 16D25, 16W50. https://nasplib.isofts.kiev.ua/handle/123456789/155239 Let R be a commutative super-ring with unity 16= 0. A proper super ideal of R is a super ideaI of R such that I 6=R.Letφ:I(R)→I(R)∪ {∅}be any function, where I(R) denotes the set of all proper super ideals of R. A homogeneous element a∈R is φ-prime to Iifra∈I−φ(I) whereris a homogeneous element in R, then r∈I. We denote byνφ(I) the set of all homogeneous elements in R that are notφ-prime to I. We define Ito beφ-primal if the set P=([(νφ(I))0+ (νφ(I))1∪ {0}] +φ(I) : ifφ6=φ∅(νφ(I))0+ (νφ(I))1: ifφ=φ∅forms a super ideal of R. For example if we takeφ∅(I) =∅(resp.φ0(I) = 0), aφ-primal superideal is a primal super ideal (resp., a weakly primal super ideal). In this paper we study several generalizations of primal super ideals of R and their properties. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Generalization of primal superideals Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Generalization of primal superideals |
| spellingShingle |
Generalization of primal superideals Jaber, A. |
| title_short |
Generalization of primal superideals |
| title_full |
Generalization of primal superideals |
| title_fullStr |
Generalization of primal superideals |
| title_full_unstemmed |
Generalization of primal superideals |
| title_sort |
generalization of primal superideals |
| author |
Jaber, A. |
| author_facet |
Jaber, A. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
Let R be a commutative super-ring with unity 16= 0. A proper super ideal of R is a super ideaI of R such that I 6=R.Letφ:I(R)→I(R)∪ {∅}be any function, where I(R) denotes the set of all proper super ideals of R. A homogeneous element a∈R is φ-prime to Iifra∈I−φ(I) whereris a homogeneous element in R, then r∈I. We denote byνφ(I) the set of all homogeneous elements in R that are notφ-prime to I. We define Ito beφ-primal if the set P=([(νφ(I))0+ (νφ(I))1∪ {0}] +φ(I) : ifφ6=φ∅(νφ(I))0+ (νφ(I))1: ifφ=φ∅forms a super ideal of R. For example if we takeφ∅(I) =∅(resp.φ0(I) = 0), aφ-primal superideal is a primal super ideal (resp., a weakly primal super ideal). In this paper we study several generalizations of primal super ideals of R and their properties.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155239 |
| citation_txt |
Generalization of primal superideals / A. Jaber // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 202-213. — Бібліогр.: 13 назв. — англ. |
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2025-12-07T16:30:31Z |
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