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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2007.1
- 수록면
- 473 - 480 (8page)
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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.
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참고문헌 (7)
참고문헌 신청
F. Alarcan / 2000 / Fully prime semirings 40 : 239 ~ 245
J. Ahsan / 1993 / Representation of weakly regular semirings by sections in a presheaf Comm. in Algebra : 2819 ~ 2835
J. Ahsan / 2001 / Prime and semiprime acts over monoids with zero 33 : 9 ~ 15
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 / 1971 / On one sided ideals of a prime type : 321 ~ 329
J. Ahsan / 1993 / Representation of weakly regular semirings by sections in a presheaf Comm. in Algebra : 2819 ~ 2835
J. Ahsan / 2001 / Prime and semiprime acts over monoids with zero 33 : 9 ~ 15
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 / 1971 / On one sided ideals of a prime type : 321 ~ 329
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