Generalization of primal superideals

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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Дата:2016
Автор: Jaber, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2016
Назва видання:Algebra and Discrete Mathematics
Онлайн доступ:http://dspace.nbuv.gov.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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1552392019-06-17T01:28:21Z Generalization of primal superideals Jaber, A. 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. 2016 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155239 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Jaber, A.
spellingShingle Jaber, A.
Generalization of primal superideals
Algebra and Discrete Mathematics
author_facet Jaber, A.
author_sort Jaber, A.
title Generalization of primal superideals
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
publisher Інститут прикладної математики і механіки НАН України
publishDate 2016
url http://dspace.nbuv.gov.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.
series Algebra and Discrete Mathematics
work_keys_str_mv AT jabera generalizationofprimalsuperideals
first_indexed 2023-05-20T17:46:25Z
last_indexed 2023-05-20T17:46:25Z
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