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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Zugang: | 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 |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862697489588551680 |
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| author | Jaber, A. |
| author_facet | Jaber, A. |
| citation_txt | Generalization of primal superideals / A. Jaber // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 202-213. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-12-07T16:30:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155239 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:30:31Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Generalization of primal superideals Jaber, A. |
| title | Generalization of primal superideals |
| title_full | Generalization of primal superideals |
| title_fullStr | Generalization of primal superideals |
| title_full_unstemmed | Generalization of primal superideals |
| title_short | Generalization of primal superideals |
| title_sort | generalization of primal superideals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155239 |
| work_keys_str_mv | AT jabera generalizationofprimalsuperideals |