{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:53:39Z","timestamp":1753883619093,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,6,30]],"date-time":"2011-06-30T00:00:00Z","timestamp":1309392000000},"content-version":"vor","delay-in-days":180,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We introduce in this paper the concept of left <jats:italic>W<\/jats:italic><jats:italic>M<\/jats:italic><jats:italic>C<\/jats:italic>2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left <jats:italic>H<\/jats:italic><jats:italic>I<\/jats:italic> rings can be extended to left <jats:italic>W<\/jats:italic><jats:italic>M<\/jats:italic><jats:italic>C<\/jats:italic>2 rings. As applications, we are able to give some new characterizations of regular left self\u2010injective rings with nonzero socle and extend some known results on strongly regular rings.<\/jats:p>","DOI":"10.1155\/2011\/294301","type":"journal-article","created":{"date-parts":[[2011,6,30]],"date-time":"2011-06-30T21:41:12Z","timestamp":1309470072000},"update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Left <i>W<\/i><i>M<\/i><i>C<\/i>2 Rings"],"prefix":"10.1155","volume":"2011","author":[{"given":"Junchao","family":"Wei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,6,30]]},"reference":[{"key":"e_1_2_3_1_2","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.6796"},{"key":"e_1_2_3_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10114\u2010004\u20100416\u20101"},{"key":"e_1_2_3_3_2","first-page":"303","article-title":"Certain rings whose simple singular modules are n\n                  i\n                  l-injective","volume":"32","author":"Wei J. 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