Next Article in Journal
Non-Coercive Radially Symmetric Variational Problems: Existence, Symmetry and Convexity of Minimizers
Previous Article in Journal
Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space
Previous Article in Special Issue
Eventually DSDD Matrices and Eigenvalue Localization
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle

Isomorphism Theorems in the Primary Categories of Krasner Hypermodules

1
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran P.O. Box 14155-6455, Iran
2
Department of Mathematics, Computer Science and Physics, University of Udine, 33100 Udine, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(5), 687; https://doi.org/10.3390/sym11050687
Received: 24 April 2019 / Revised: 13 May 2019 / Accepted: 16 May 2019 / Published: 18 May 2019
(This article belongs to the Special Issue Symmetry in Numerical Linear and Multilinear Algebra)
PDF [279 KB, uploaded 18 May 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 ) } .
Keywords: Krasner hyperring; Krasner hypermodule; isomorphism theorem; factorization theorem; category theory Krasner hyperring; Krasner hypermodule; isomorphism theorem; factorization theorem; category theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Shojaei, H.; Fasino, D. Isomorphism Theorems in the Primary Categories of Krasner Hypermodules. Symmetry 2019, 11, 687.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top