Počet záznamů: 1
Topologically semisimple and topologically perfect topological rings
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SYSNO ASEP 0558266 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Topologically semisimple and topologically perfect topological rings Tvůrce(i) Positselski, Leonid (MU-W) SAI, ORCID, RID
Šťovíček, J. (CZ)Zdroj.dok. Publicacions Matematiques. - : Universidad Autonoma de Madrid - ISSN 0214-1493
Roč. 66, č. 2 (2022), s. 457-540Poč.str. 84 s. Jazyk dok. eng - angličtina Země vyd. ES - Španělsko Klíč. slova discrete modules and contramodules ; projective covers ; modules with perfect decomposition Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Způsob publikování Open access Institucionální podpora MU-W - RVO:67985840 UT WOS 000830838900002 EID SCOPUS 85133329381 DOI 10.5565/PUBLMAT6622202 Anotace Extending the Wedderburn-Artin theory of semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split (equivalently, semisimple) if and only if the abelian category of discrete right modules over the same ring is split (equivalently, semisimple). An extension of the Bass theory of left perfect rings to the topological realm is formulated as a list of conjecturally equivalent conditions, many equivalences and implications between which we prove. In particular, all the conditions are equivalent for topological rings with a countable base of neighborhoods of zero. We establish a connection between the concept of a topologically perfect topological ring and the theory of modules with perfect decomposition and show that a countably generated module Sigma-coperfect over its endomorphism ring has a perfect decomposition, partially answering a question of Angeleri Hugel and Saorin. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2023 Elektronická adresa https://dx.doi.org/10.5565/PUBLMAT6622202
Počet záznamů: 1