ISSN: 1304-7191 | E-ISSN: 1304-7205
Krasner hypermodules of generalized fractions
1Department of Mathematics, Yazd University, Yazd-IRAN
Sigma J Eng Nat Sci 2018; 9(): 39-62
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In this paper, we define the Krasner hypermodule of generalized fractions of a hypermodule M over a Krasner hyperring R . If M is an R -hypermodule, then we construct the Krasner hypermodule of generalized fractions U -nM consisting of all fractions m with m M and u1,...,un U . u1 ,...,un  We show that U -n M is a Krasner hypermodule. Then, we consider the category of Krasner hypermodules and prove that the direct limit always exists. We consider the fundamental equivalence relation εu* and prove some results about the connections between the Krasner hypermodule of fractions and the fundamental Krasner modules, direct systems and direct limits.