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Strongly Prime Ideals and Primal Ideals in Posets
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In this paper, we study and establish some interesting results of ideals in a poset. It is shown that for a nonzero ideal $I$ of a poset $P$, there are at most two strongly prime ideals of $P$ that are minimal over $I$. Also, we study the notion of primal ideals in a poset and the relationship among the primal ideals and strongly prime ideals is considered.
Abstract
In this paper, we study and establish some interesting results of ideals in a poset. It is shown that for a nonzero ideal $I$ of a poset $P$, there are at most two strongly prime ideals of $P$ that are minimal over $I$. Also, we study the notion of primal ideals in a poset and the relationship among the primal ideals and strongly prime ideals is considered.
참고문헌 (10)
- J. Catherine Grace John, "Primeness of extension of semi-ideals in posets", Applied Mathematical Sciences, 164(8), pp.8227~8232 (2014)
- J. Catherine Grace John, "zJ -ideals and strongly prime ideals in posets", ~
- J. Catherine Grace John, "Strongly prime and strongly semiprime ideals in Posets", Global Journal of Pure and Applied Mathematics, 11(5), pp.2965~2970 (2015)
- L. Fuchs, "On primal ideals", Proc. Amer. Math. Soc., 1, pp.1~6 (1950)
- L. Fuchs, "Commutative ideal theory without finiteness conditions: Primal ideal", Trans. Amer. Math. Soc., 357(7), pp.2771~2798 (2004)
- R. Halas, "On extension of ideals in posets", Discrete Mathematics, 308, pp.4972~4977 (2008)
- G. H. Jiang, "Maximal ideals relative to a filter on posets and some applications", Int. J. Contemp. Math. Sciences, 3(9), pp.401~410 (2008)
- Jan Paseka, "Note on distributive posets", Math. Appl., 1, pp.197~206 (2012)
- V. S. Kharat, "Primeness and semiprimeness in posets", Math. Bohem., 134(1), pp.19~30 (2009)
- P. V. Venkatanarasimhan, "Semi ideals in posets", Math. Ann., 185(4), pp.338~348 (1970)
관련 논문AI추천
zJ− Ideals and Strongly Prime Ideals in PosetsBalasubramanian Elavarasan, Catherine Grace John경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제3호Poset Properties Determined by the Ideal - Based Zero-divisor GraphBalasubramanian Elavarasan, Kasi Porselvi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제2호$L$-fuzzy prime ideals and maximal $L$-fuzzy ideals of a posetBerhanu Assaye Alaba, Derso Abeje Engidaw, Mihret Alamneh Taye기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2019 · 제18권 제1호ON L-FUZZY SEMI-PRIME IDEALS OF A POSET AND SEPARATION THEOREMSDerso Abeje Engidaw, Tilahun Bimerew Alemu강원경기수학회 · 한국수학논문집2021 · 제29권 제2호L-fuzzy ideals of a posetBerhanu Assaye Alaba, Derso Abeje Engidaw, Miheret Alamneh Taye기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2018 · 제16권 제3호An ideal - based zero-divisor graph of posetsBalasubramanian Elavarasan, Kasi Porselvi대한수학회 · 대한수학회논문집2013 · 제28권 제1호
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