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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2009.1
- 수록면
- 221 - 233 (13page)
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초록· 키워드
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In this article, we generalize a well-known result of Hebisch and Weinert that
states that a finite semidomain is either zerosumfree or a ring. Specifically, we show that
the class of commutative semirings S such that S has nonzero characteristic and every
zero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. In
addition, we demonstrate that if S is a finite commutative semiring such that the set of
zero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpotent
or S must be a ring. An example is given to establish the existence of semirings in this
latter category with both nontrivial zero-sums and zero-divisors that are not nilpotent.
목차
등록된 정보가 없습니다.
참고문헌 (14)
참고문헌 신청
A. J. Hetzel / 2004 / Quasi-going-up rings / Houston J. Math 30 : 357 ~ 392
D. E. Dobbs / 2006 / On integrally closed going-down rings / Int. J. Math. Game Theory Algebra 15 : 155 ~ 165
D.E. Dobbs / 1997 / Going-down rings with zero-divisors / Houston J. Math 23 : 1 ~ 12
F. Alarc´on / 1994 / Commutative semirings and their lattices of ideals / Houston J. Math 20 : 571 ~ 590
I. Kaplansky / 1974 / Commutative Rings / Univ. Chicago Press
D. E. Dobbs / 2006 / On integrally closed going-down rings / Int. J. Math. Game Theory Algebra 15 : 155 ~ 165
D.E. Dobbs / 1997 / Going-down rings with zero-divisors / Houston J. Math 23 : 1 ~ 12
F. Alarc´on / 1994 / Commutative semirings and their lattices of ideals / Houston J. Math 20 : 571 ~ 590
I. Kaplansky / 1974 / Commutative Rings / Univ. Chicago Press
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