BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:iCalendar-Ruby BEGIN:VEVENT CATEGORIES:Lectures & Presentations DESCRIPTION:Ring Theory Seminar | On Simple-Direct Modules\, April 9\n\nThe Ohio University-Ohio State University Ring Theory Seminar Series presents Engin Büyükaşık of the Izmir Institute of Technology\, discussing "On Simpl e-Direct Modules" on Friday\, April 9\, at 3 p.m.\n\nJoin Zoom Meeting: htt ps://osu.zoom.us/j/97614086322?pwd=SnJWYStwVC9KYzZhbzdDZWtiRU5HQT09Meeting ID: 976 1408 6322Password: 314159\n\nOne tap mobile\n\n+16468769923\,\,9761 4086322#\,\,\,\,0#\,\,314159# US (New York)\n\n+16513728299\,\,97614086322# \,\,\,\,0#\,\,314159# US (Minnesota)\n\nFor more information\, contact Serg io Lopez-Permouth\, professor of Mathematics at Ohio University.\n\nAbstrac t: A right module M is called direct-injective (or C2) if every submodule i somorphic to a summand of M is itself a summand. Dually\, a module M is cal led direct-projective (or D2) if for every submodule N of M with M/N isomor phic to summand of M\, then N is a summand of M. Recently\, in a series of papers “simple” versions of the aforementioned modules have been investigat ed ([3]\, [4]\, [5]). These modules are termed as “simple-direct-injective” and “simple-direct-projective\,” respectively.\n\nIn this talk\, we shall discuss the structure of these modules over certain rings including the rin g of integers. Besides\, it will be shown that the rings whose simple-direc t-injective right modules are simple-direct-projective are exactly the left perfect right H-rings\, and that\, for a commutative Noetherian ring\, sim ple-direct-projective modules are simple-direct-injective if and only if si mple-direct-injective modules are simple-direct-projective if and only if t he ring is Artinian. These results are recently appeared in [1].\n\nReferen ces\n\n[1] B¨uy¨uka¸sık\, E.\, Demir\, O.\, Diril\, M. (2021). On simple-di rect modules. ¨ Comm. Algebra 49:864-876.\n\n[2] Camillo\, V. (1978). Homol ogical independence of injective hulls of simple modules over commutative r ings\, Comm. Algebra 6:1459-1469.\n\n[3] Camillo\, V.\, Ibrahim\, Y.\, Yous if\, M.\, Zhou\, Y. (2014). Simple-direct-injective modules\, J. Algebra 42 0:39-53.\n\n[4] Ibrahim\, Y.\, Ko¸san\, M. T.\, Quynh\, T. C.\, Yousif\, M. (2016). Simple-Direct-Projective Modules. Comm. Algebra 44:5163-5178.\n\n[ 5] Ibrahim\, Y.\, Ko¸san\, M. T.\, Quynh\, T. C.\, Yousif\, M. (2017). Simp le-direct-modules. Comm. Algebra 45:3643-3652. DTEND:20210409T200000Z DTSTAMP:20240921T072949Z DTSTART:20210409T190000Z LOCATION: SEQUENCE:0 SUMMARY:Ring Theory Seminar | On Simple-Direct Modules\, April 9 UID:tag:localist.com\,2008:EventInstance_36349825580222 URL:https://calendar.ohio.edu/event/ring_theory_seminar_on_simple-direct_mo dules_april_9 END:VEVENT END:VCALENDAR