논문KCI 등재
One-sided Prime Ideals in Semirings
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Abstract
In this paper we define prime right ideals of semirings and prove that if every right ideal of a semiring R is prime then R is weakly regular. We also prove that if the set of right ideals of R is totally ordered then every right ideal of R is prime if and only if R is right weakly regular. Moreover in this paper we also define prime subsemimodule (generalizing the concept of prime right ideals) of an R-semimodule. We prove that if a subsemimodule K of an R-semimodule M is prime then AK(M) is also a prime ideal of R.
참고문헌 (7)
- J. Ahsan, "Representation of weakly regular semirings by sections in a presheaf Comm. in Algebra", pp.2819~2835 (1993)
- J. Ahsan, "Prime and semiprime acts over monoids with zero", 33, pp.9~15 (2001), Ibaraki University
- F. Alarcan, "Fully prime semirings", 40, pp.239~245 (2000)
- W. D. Blair, "Fully prime rings", 22(13), pp.5389~5400 (1994)
- Publ. Math. Debrecen, "Radicals of the semiring of abelian groups", pp.89~90 (1980)
- J. S. Golan, "The Theory of Semiring with Applications in Mathematics and Theoretical Computer Science Pitman Monographs and Surveys in Pure and App. Math."
- K. Koh, "On one sided ideals of a prime type", pp.321~329 (1971)
관련 논문AI추천
Ideal Theory in Commutative A-semiringsHee Sik Kim, Joseph Neggers, Paul J. Allen경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제2호On Partitioning Ideals of SemiringsJayprakash Ninu Chaudhari, Vishnu Gupta경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제2호Fuzzy 2-(0- or 1-)prime ideals in semiringsP. Dheena, S. Coumaressane대한수학회 · 대한수학회보2006 · 제43권 제3호1-(2-) Prime Ideals in SemiringsPandarinathan Nandakumar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제1호Primitive Ideals of Semigroup Graded RingsHema Gopalakrishnan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제4호On Semirings which are Distributive Lattices of RingsS. K. Maity경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제1호
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