Document Type : Original Manuscript
Authors
1 Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran.
2 School of Mathematics, Statistics and Computer Sciences, University of Tehran, P.O. Box 14155-6455, Tehran, Iran.
Abstract
In this paper, we construct the concept of general Krasner hyperring based on the ring structures and the left general Krasner hypermodule based on the module structures. This study introduces the trivial left general Krasner hypermodules and proves that the trivial left general Krasner hypermodules are different from left Krasner hypermodules. We show that for any given general Krasner hyperring $R$ and trivial left general Krasner hypermodules $A, B, {\bf_{R}h}$om$(A, B)$ is a left general Krasner hypermodule and ${\bf_{R}h}$om$(-, B)$, $ ({\bf_{R}h}$om$(A, -) )$ is an exact covariant functor (contravariant). Finally, we show that the category ${\bf_{R}GKH}$mod (left trivial general Krasner hypermodules and all (homomorphisms) is an abelian category and trivial left general Krasner hypermodules have a normal injective resolution.
Keywords
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