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On Partitioning and Subtractive Subsemimodules of Semimodules over Semirings

Chaudhari, Jaiprakash Ninu;Bond, Dipak Ravindra

  • Received : 2009.12.02
  • Accepted : 2010.05.14
  • Published : 2010.06.30

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 ${\rightarrow}$ M' is a maximal R-semimodule homomorphism, then $M/kerf_{(Q)}\;\cong\;M'$. 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 $N{\subseteq}A$ if and only if $A/N_{(Q{\cap}A)}\;=\;\{q+N:q{\in}Q{\cap}A\}$ is a subtractive subsemimodule of $M/N_{(Q)}$.

Keywords

semimodule;subtractive subsemimodule;partitioning subsemimodule;quotient semimodule;maximal homomorphism;isomorphism

References

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Cited by

  1. On Exact Sequence of Semimodules over Semirings vol.2013, 2013, https://doi.org/10.1155/2013/156485
  2. ON SUBTRACTIVE EXTENSION OF SUBSEMIMODULES OF SEMIMODULES vol.26, pp.1, 2013, https://doi.org/10.14403/jcms.2013.26.1.037