{"id":813,"date":"2019-10-10T00:00:46","date_gmt":"2019-10-10T00:00:46","guid":{"rendered":"http:\/\/mat.uab.cat\/web\/perera\/?p=813"},"modified":"2020-03-11T10:04:27","modified_gmt":"2020-03-11T10:04:27","slug":"ring-theory-seminar","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/perera\/2019\/10\/10\/ring-theory-seminar\/","title":{"rendered":"Seminar (Ring Theory)"},"content":{"rendered":"\n<p><a href=\"https:\/\/www.math.unipd.it\/en\/department\/people\/user.php?usertype=4&amp;user=886\" target=\"_blank\" rel=\"noopener\">Giovanna Le Gros<\/a> (Universit\u00e0 di Padova) delivered the talk:<\/p>\n\n\n\n<p><em>Minimal approximations and 1-tilting cotorsion pairs over commutative rings<\/em><\/p>\n\n\n\n<p>Abstract:<\/p>\n\n\n\n<p>Minimal approximations of modules, or covers and envelopes of modules, were introduced as a tool to approximate modules by classes of modules which are more manageable. For a class C of R-modules, the aim is to characterise the rings over which every module has a C-cover or C-envelope. Moreover A-precovers and B-preenvelopes are strongly related to the notion of a cotorsion pair (A,B).<\/p>\n\n\n\n<p>In this talk we are interested in the particular case that (P_1,B) is the cotorsion pair generated by the modules of projective dimension at most one (denoted P_1) over commutative rings. More precisely, we investigate over which rings these cotorsion pairs admit covers or envelopes. Furthermore, we interested in Enochs&#8217; Conjecture in this setting, that is if P_1 is covering necessarily implies that it is closed under direct limits. The investigation of the cotorsion pair (P_1,B) splits into two cases: when the cotorsion pair is of finite type and when it is not. In this talk I will outline some results for the case that the cotorsion pair is of finite type, where we consider more generally a 1-tilting cotorsion pair over a commutative ring.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Giovanna Le Gros (Universit\u00e0 di Padova) delivered the talk: Minimal approximations and 1-tilting cotorsion pairs over commutative rings Abstract: Minimal approximations of modules, or covers and envelopes of modules, were introduced as a tool to approximate modules by classes of modules which are more manageable. For a class C of R-modules, the aim is to &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/mat.uab.cat\/web\/perera\/2019\/10\/10\/ring-theory-seminar\/\" class=\"more-link\">Continua llegint <span class=\"screen-reader-text\">\u00abSeminar (Ring Theory)\u00bb<\/span><\/a><\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,3],"tags":[],"class_list":["post-813","post","type-post","status-publish","format-standard","hentry","category-ring-theory","category-seminars"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/posts\/813","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/comments?post=813"}],"version-history":[{"count":5,"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/posts\/813\/revisions"}],"predecessor-version":[{"id":829,"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/posts\/813\/revisions\/829"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/media?parent=813"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/categories?post=813"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/perera\/wp-json\/wp\/v2\/tags?post=813"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}