NORMAL INJECTIVE RESOLUTION OF GENERAL KRASNER HYPERMODULES | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 1، آذر 2022، صفحه 121-145 اصل مقاله (226.69 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.10188.1505 | ||
| نویسندگان | ||
| M. Hamidi* 1؛ F. Faraji1؛ R. Ameri2؛ Kh. Ahmadi-amoli1 | ||
| 1Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. | ||
| 2School of Mathematics, Statistics and Computer Sciences, University of Tehran, P.O. Box 14155-6455, Tehran, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Keywords: General Krasner hyperrings؛ (normal injective) left general Krasner hypermodules؛ normal injective resolution؛ abelian category | ||
| مراجع | ||
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