Prime Spectrum and Relations on Krasner Hypermodules

Prime Spectrum and Relations on Krasner Hypermodules | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 14 April 2025 V1 Latest version Share on Prime Spectrum and Relations on Krasner Hypermodules Authors : Behnam Afshar 0009-0006-7095-5795 [email protected] and Reza Ameri Authors Info & Affiliations https://doi.org/10.22541/au.174465640.07378624/v1 128 views 78 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We study the Zariski topology of Krasner hypermodules from the perspective of regular relations. To this end, we first examine the main properties of the Zariski topology of hypermodules and investigate its connection with the classical case. In the next step, we prove results regarding the relationship between relations on the R-hypermodule M, and relations on the hypergroup M and the hyperring R. We then show that, (strongly) regular relations on a hypermodule and specific subhypermodules form isomorphic lattices. This results will also be examined for quotient hypermodules. Next, we define prime and primary relations on hypermodules and examine their properties. These properties help us introduce a topology based on relations, which plays an important role in the study of sheaves of hypermodules. Supplementary Material File (prime spectrum and relations on krasner hypermodules.pdf) Download 175.81 KB Information & Authors Information Version history V1 Version 1 14 April 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords fundamental relation krasner hypermodule prime relation regular relation zariski topology Authors Affiliations Behnam Afshar 0009-0006-7095-5795 [email protected] Department of Mathematics, Statistics and Computer Science, College of Science, University of Tehran View all articles by this author Reza Ameri Department of Mathematics, Statistics and Computer Science, College of Science, University of Tehran View all articles by this author Metrics & Citations Metrics Article Usage 128 views 78 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Behnam Afshar, Reza Ameri. Prime Spectrum and Relations on Krasner Hypermodules. Authorea . 14 April 2025. DOI: https://doi.org/10.22541/au.174465640.07378624/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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