On Partitioning and Subtractive Subsemimodules of Semi- modules over Semirings
1
조회
0
다운로드
2
인용
0
참고문헌
초록
In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M/N(Q) is essentially independent of choice of Q. 2) If f : M -> M′ is a maximal R-semimodule homomorphism, then M/kerf(Q) = M′ . 3)Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with N ⊆A if and only if A/N(Q∩A) = {q + N : q ∈Q ∩A}is a subtractive subsemimodule of M/N(Q).
Abstract
In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M/N(Q) is essentially independent of choice of Q. 2) If f : M -> M′ is a maximal R-semimodule homomorphism, then M/kerf(Q) = M′ . 3)Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with N ⊆A if and only if A/N(Q∩A) = {q + N : q ∈Q ∩A}is a subtractive subsemimodule of M/N(Q).
참고문헌 (8)
- Paul J. Allen, "fundamental theorem of homomorphism for semirings", Proc. Amer. Math. Soc., 21, pp.412~416 (1969)
- Paul J. Allen, "Ideal Theory in Commutative A-semirings", Kyungpook Mathematical Journal, 46(2), pp.261~271 (2006), 경북대학교 자연과학대학 수학과
- R. E. Atani, "On subsemimodules of semimodules", Buletinul Acad. Sci. Republ. Moldova, ser. Math. (2010)
- Shahabaddin Ebrahimi Atani, "The ideal theory in quotient of commutative semirings", Glasnik Matematicki, 42(62), pp.301~308 (2007)
- J. S. Golan, "Semiring and their Applications" (1999), Kluwer Academic publisher Dordrecht
- Vishnu Gupta, "On Right π-Regular Semirings", Sarajevo Journal of Mathematics, 2(14), pp.3~9 (2006)
- Vishnu Gupta, "On Partitioning Ideals of Semirings", Kyungpook Mathematical Journal, 46(2), pp.181~184 (2006), 경북대학교 자연과학대학 수학과
- Vishnu Gupta, "Some remarks on semirings", Radovi Matematicki, 12, pp.13~18 (2003)