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Isomorphism Theorems in the Primary Categories of Krasner Hypermodules
- Source :
- Symmetry, Vol 11, Iss 5, p 687 (2019)
- Publication Year :
- 2019
- Publisher :
- MDPI AG, 2019.
-
Abstract
- Let R be a Krasner hyperring. In this paper, we prove a factorization theorem in the category of Krasner R-hypermodules with inclusion single-valued R-homomorphisms as its morphisms. Then, we prove various isomorphism theorems for a smaller category, i.e., the category of Krasner R-hypermodules with strong single-valued R-homomorphisms as its morphisms. In addition, we show that the latter category is balanced. Finally, we prove that for every strong single-valued R-homomorphism f : A → B and a ∈ A , we have K e r ( f ) + a = a + K e r ( f ) = { x ∈ A ∣ f ( x ) = f ( a ) } .
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 11
- Issue :
- 5
- Database :
- Directory of Open Access Journals
- Journal :
- Symmetry
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.087286e7a6514358add710e9a3a7a4d3
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/sym11050687