On Partitioning and Subtractive Subsemimodules of Semimodules over Semirings

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 2,  2010, pp.329-336
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.2.329
Title & Authors
On Partitioning and Subtractive Subsemimodules of Semimodules over Semirings
Chaudhari, Jaiprakash Ninu; Bond, Dipak Ravindra;

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 $\small{{\rightarrow}}$ M' is a maximal R-semimodule homomorphism, then $\small{M/kerf_{(Q)}\;\cong\;M$. 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 $\small{N{\subseteq}A}$ if and only if $\small{A/N_{(Q{\cap}A)}\;=\;\{q+N:q{\in}Q{\cap}A\}}$ is a subtractive subsemimodule of $\small{M/N_{(Q)}}$.
Keywords
semimodule;subtractive subsemimodule;partitioning subsemimodule;quotient semimodule;maximal homomorphism;isomorphism;
Language
English
Cited by
1.
ON SUBTRACTIVE EXTENSION OF SUBSEMIMODULES OF SEMIMODULES, Journal of the Chungcheng Mathematical Society, 2013, 26, 1, 37
2.
On Exact Sequence of Semimodules over Semirings, ISRN Algebra, 2013, 2013, 1
References
1.
Paul J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21(1969), 412-416.

2.
Paul J. Allen, J. Neggers and H. S. Kim, Ideal theory in commutative A-semirings, Kyungpook. Math. Journal, 46(2006), 261-271.

3.
R. E. Atani and S. E. Atani, On subsemimodules of semimodules, Buletinul Acad. Sci. Republ. Moldova, ser. Math., to appear (2010).

4.
Shahabaddin Ebrahimi Atani, The ideal theory in quotient of commutative semirings, Glasnik Matematicki, Vol. 42(62)(2007), 301-308.

5.
J. S. Golan, Semiring and their Applications, Kluwer Academic publisher Dordrecht, 1999.

6.
Vishnu Gupta and J. N. Chaudhari, On Right $\pi$-Regular Semirings, Sarajevo Journal of Mathematics. Vol 2(14)(2006), 3-9.

7.
Vishnu Gupta and J. N. Chaudhari, On Partitioning ideals of Semirings, Kyungpook. Math. Journal, 46(2006), 181-184.

8.
Vishnu Gupta and J. N. Chaudhari, Some remarks on semirings, Radovi Matematicki, 12(2003), 13-18.