On some structural properties of evolution algebras

We consider the intersection \(\mathfrak{M}(A)\) of all maximal ideals of an evolution algebra \(A\) and study the structure of the quotient \(A/\M(A)\). In a previous work, maximal ideals have been related to hereditary subsets of a graph associated to the given algebra. We investigate the superflu...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Yolanda Cabrera Casado, Dolores Martín Barquero, Cándido Martín González, Tocino, Alicia
Format: Article
Language:English
Subjects:
Algebra
Evolution
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Yolanda Cabrera Casado
Dolores Martín Barquero
Cándido Martín González
Tocino, Alicia
description We consider the intersection \(\mathfrak{M}(A)\) of all maximal ideals of an evolution algebra \(A\) and study the structure of the quotient \(A/\M(A)\). In a previous work, maximal ideals have been related to hereditary subsets of a graph associated to the given algebra. We investigate the superfluous members both in the family of maximal ideals and also in the set of hereditary subsets of the associated graphs. By using subdirect products we state a structure theorem for arbitrary evolution algebras (arbitrary dimensions and ground field). Specializing in the perfect finite-dimensional case, we obtain a direct sum decomposition instead of a subdirect product and also a uniqueness property. We also study some examples in which Grassmanians appear in a natural way and others that exhibit a richer structure with a nonzero semisimple part that is non-associative.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2885375371</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2885375371</sourcerecordid><originalsourceid>FETCH-proquest_journals_28853753713</originalsourceid><addsrcrecordid>eNqNi0EKwjAQRYMgWLR3CLgupDPGZi-KOzfuS5RpaYlJzSSe3yw8gPDhLd77K1EBYtuYA8BG1MyzUgqOHWiNlcCblxxeJDnF_Ew5WieXGBaKaSKWYZD0CS6nKXhp3UiPaHkn1oN1TPWPW7G_nO-na1OO70yc-jnk6IvqwRiNXVmL_1VfZNY07A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2885375371</pqid></control><display><type>article</type><title>On some structural properties of evolution algebras</title><source>ProQuest - Publicly Available Content Database</source><creator>Yolanda Cabrera Casado ; Dolores Martín Barquero ; Cándido Martín González ; Tocino, Alicia</creator><creatorcontrib>Yolanda Cabrera Casado ; Dolores Martín Barquero ; Cándido Martín González ; Tocino, Alicia</creatorcontrib><description>We consider the intersection \(\mathfrak{M}(A)\) of all maximal ideals of an evolution algebra \(A\) and study the structure of the quotient \(A/\M(A)\). In a previous work, maximal ideals have been related to hereditary subsets of a graph associated to the given algebra. We investigate the superfluous members both in the family of maximal ideals and also in the set of hereditary subsets of the associated graphs. By using subdirect products we state a structure theorem for arbitrary evolution algebras (arbitrary dimensions and ground field). Specializing in the perfect finite-dimensional case, we obtain a direct sum decomposition instead of a subdirect product and also a uniqueness property. We also study some examples in which Grassmanians appear in a natural way and others that exhibit a richer structure with a nonzero semisimple part that is non-associative.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Evolution</subject><ispartof>arXiv.org, 2023-12</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2885375371?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>776,780,25731,36989,44566</link.rule.ids></links><search><creatorcontrib>Yolanda Cabrera Casado</creatorcontrib><creatorcontrib>Dolores Martín Barquero</creatorcontrib><creatorcontrib>Cándido Martín González</creatorcontrib><creatorcontrib>Tocino, Alicia</creatorcontrib><title>On some structural properties of evolution algebras</title><title>arXiv.org</title><description>We consider the intersection \(\mathfrak{M}(A)\) of all maximal ideals of an evolution algebra \(A\) and study the structure of the quotient \(A/\M(A)\). In a previous work, maximal ideals have been related to hereditary subsets of a graph associated to the given algebra. We investigate the superfluous members both in the family of maximal ideals and also in the set of hereditary subsets of the associated graphs. By using subdirect products we state a structure theorem for arbitrary evolution algebras (arbitrary dimensions and ground field). Specializing in the perfect finite-dimensional case, we obtain a direct sum decomposition instead of a subdirect product and also a uniqueness property. We also study some examples in which Grassmanians appear in a natural way and others that exhibit a richer structure with a nonzero semisimple part that is non-associative.</description><subject>Algebra</subject><subject>Evolution</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNi0EKwjAQRYMgWLR3CLgupDPGZi-KOzfuS5RpaYlJzSSe3yw8gPDhLd77K1EBYtuYA8BG1MyzUgqOHWiNlcCblxxeJDnF_Ew5WieXGBaKaSKWYZD0CS6nKXhp3UiPaHkn1oN1TPWPW7G_nO-na1OO70yc-jnk6IvqwRiNXVmL_1VfZNY07A</recordid><startdate>20231222</startdate><enddate>20231222</enddate><creator>Yolanda Cabrera Casado</creator><creator>Dolores Martín Barquero</creator><creator>Cándido Martín González</creator><creator>Tocino, Alicia</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20231222</creationdate><title>On some structural properties of evolution algebras</title><author>Yolanda Cabrera Casado ; Dolores Martín Barquero ; Cándido Martín González ; Tocino, Alicia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_28853753713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Evolution</topic><toplevel>online_resources</toplevel><creatorcontrib>Yolanda Cabrera Casado</creatorcontrib><creatorcontrib>Dolores Martín Barquero</creatorcontrib><creatorcontrib>Cándido Martín González</creatorcontrib><creatorcontrib>Tocino, Alicia</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Engineering Database</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>ProQuest - Publicly Available Content Database</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied &amp; Life Sciences</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yolanda Cabrera Casado</au><au>Dolores Martín Barquero</au><au>Cándido Martín González</au><au>Tocino, Alicia</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>On some structural properties of evolution algebras</atitle><jtitle>arXiv.org</jtitle><date>2023-12-22</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>We consider the intersection \(\mathfrak{M}(A)\) of all maximal ideals of an evolution algebra \(A\) and study the structure of the quotient \(A/\M(A)\). In a previous work, maximal ideals have been related to hereditary subsets of a graph associated to the given algebra. We investigate the superfluous members both in the family of maximal ideals and also in the set of hereditary subsets of the associated graphs. By using subdirect products we state a structure theorem for arbitrary evolution algebras (arbitrary dimensions and ground field). Specializing in the perfect finite-dimensional case, we obtain a direct sum decomposition instead of a subdirect product and also a uniqueness property. We also study some examples in which Grassmanians appear in a natural way and others that exhibit a richer structure with a nonzero semisimple part that is non-associative.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2023-12
issn 2331-8422
language eng
recordid cdi_proquest_journals_2885375371
source ProQuest - Publicly Available Content Database
subjects Algebra
Evolution
title On some structural properties of evolution algebras
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-24T01%3A37%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=On%20some%20structural%20properties%20of%20evolution%20algebras&rft.jtitle=arXiv.org&rft.au=Yolanda%20Cabrera%20Casado&rft.date=2023-12-22&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2885375371%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_28853753713%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2885375371&rft_id=info:pmid/&rfr_iscdi=true