A TOPOLOGICAL APPROACH TO MORITA EQUIVALENCE FOR RINGS WITH LOCAL UNITS
In [1] and [3] a theory of Morita equivalence has recently been developed for certain not necessarily unital rings called rings with local units. In this article we prove that the special Horn-sets which figure in the description of equivalence functors are actually the sets of continuous homomorphi...
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| Veröffentlicht in: | The Rocky Mountain journal of mathematics 1992, Vol.22 (2), p.405-416 |
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| container_title | The Rocky Mountain journal of mathematics |
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| creator | ABRAMS, G.D. ÁNH, P.N. MÁRKI, L. |
| description | In [1] and [3] a theory of Morita equivalence has recently been developed for certain not necessarily unital rings called rings with local units. In this article we prove that the special Horn-sets which figure in the description of equivalence functors are actually the sets of continuous homomorphisms from a locally projective generator (endowed with a suitable topology) into discrete modules. The main result of this paper says that two rings with local units which fulfill a topological condition of projectivity are Morita equivalent if and only if suitable matrix rings over them are isomorphic to each other. |
| doi_str_mv | 10.1216/rmjm/1181072737 |
| format | Article |
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In this article we prove that the special Horn-sets which figure in the description of equivalence functors are actually the sets of continuous homomorphisms from a locally projective generator (endowed with a suitable topology) into discrete modules. The main result of this paper says that two rings with local units which fulfill a topological condition of projectivity are Morita equivalent if and only if suitable matrix rings over them are isomorphic to each other.</description><identifier>ISSN: 0035-7596</identifier><identifier>EISSN: 1945-3795</identifier><identifier>DOI: 10.1216/rmjm/1181072737</identifier><language>eng</language><publisher>The Rocky Mountain Mathematics Consortium</publisher><subject>16A42 ; 16A89 ; Algebraic topology ; Equivalence relation ; Functors ; Homomorphisms ; Mathematical rings ; Topological spaces ; Topological theorems ; Topological vector spaces ; Topology ; Vector spaces</subject><ispartof>The Rocky Mountain journal of mathematics, 1992, Vol.22 (2), p.405-416</ispartof><rights>Copyright © 1992 Rocky Mountain Mathematics Consortium</rights><rights>Copyright 1992 Rocky Mountain Mathematics Consortium</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-154aaff0b008614a2df19a2b8a82f0cf33867a94c26b59fd27e308cd59b327113</citedby><cites>FETCH-LOGICAL-c360t-154aaff0b008614a2df19a2b8a82f0cf33867a94c26b59fd27e308cd59b327113</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/44237467$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/44237467$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,803,832,885,926,4024,27923,27924,27925,58017,58021,58250,58254</link.rule.ids></links><search><creatorcontrib>ABRAMS, G.D.</creatorcontrib><creatorcontrib>ÁNH, P.N.</creatorcontrib><creatorcontrib>MÁRKI, L.</creatorcontrib><title>A TOPOLOGICAL APPROACH TO MORITA EQUIVALENCE FOR RINGS WITH LOCAL UNITS</title><title>The Rocky Mountain journal of mathematics</title><description>In [1] and [3] a theory of Morita equivalence has recently been developed for certain not necessarily unital rings called rings with local units. 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| ispartof | The Rocky Mountain journal of mathematics, 1992, Vol.22 (2), p.405-416 |
| issn | 0035-7596 1945-3795 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_rmjm_1181072737 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 16A42 16A89 Algebraic topology Equivalence relation Functors Homomorphisms Mathematical rings Topological spaces Topological theorems Topological vector spaces Topology Vector spaces |
| title | A TOPOLOGICAL APPROACH TO MORITA EQUIVALENCE FOR RINGS WITH LOCAL UNITS |
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