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Ring Theory Seminar - CANCELLED

Ring Theory Seminar
January 30, 2019
4:45PM - 5:45PM
CANCELLED

Date Range
Add to Calendar 2019-01-30 16:45:00 2019-01-30 17:45:00 Ring Theory Seminar - CANCELLED Due to the Ohio State University Columbus campus closure because of inclement weather, this seminar talk has been cancelled. Please visit Math Events for a listing of future events in the Department of Mathematics.   Title: (L-)principally quasi-Baer modules Speaker: Gangyong Lee (Chungnam National University, South Korea) Abstract: The purpose of this talk is to further the study of principally quasi-Baer modules and $\mathfrak{L}$-principally quasi-Baer modules as these properties play an important role in the study of quasi-Baer module. The notion of quasi-Baer modules in a general module theoretic setting was introduced by Rizvi and Roman [4], and then Lee and Rizvi studied the direct sum property for quasi-Baer modules, recently [2]. In addition, many other mathematicians investigated a p.q.-Baer module in a general module theoretic setting for a right p.q.-Baer ring (see [1]) as investigating that for quasi-Baer rings. First, in this talk, we provide some basic results and a characterization of a principally quasi-Baer (simply, p.q.-Baer) module in terms of its endomorphism ring by using the $pq$-local-retractable property. In addition, we fully characterize when a finite direct sum of arbitrary p.q.-Baer modules is p.q.-Baer. We obtain characterizations and properties of $\mathfrak{L}$-principally quasi-Baer (simply, $\mathfrak{L}$-p.q.-Baer) modules. Examples which show that the notion of an $\mathfrak{L}$-p.q.-Baer module is distinct from that of a p.q.-Baer module are provided. It is shown that every direct summand of an $\mathfrak{L}$-p.q.-Baer module inherits the property. Furthermore, we obtain that every direct sum of copies of an $\mathfrak{L}$-p.q.-Baer module is an $\mathfrak{L}$-p.q.-Baer module. We provide conditions when ($\mathfrak{L}$-)p.q.-Baer modules become quasi-Baer modules. In particular, if every direct sum of copies of a module $M$ is p.q.-Baer then the module $M$ is a quasi-Baer module. Works Cited G.F. Birkenmeier; J.Y. Kim; J.K. Park, Principally quasi-Baer rings, Comm. Algebra, 2001 29(2), 638--660 G. Lee; S.T. Rizvi, Direct sums of quasi-Baer modules, J. Algebra, 2016 456, 76--92 G. Lee, Principally quasi-Baer modules and their generalizations, submitted S.T. Rizvi; C.S. Roman, Baer and quasi-Baer modules, Comm. Algebra, 2004 32(1), 103--123 CANCELLED Department of Mathematics math@osu.edu America/New_York public

Due to the Ohio State University Columbus campus closure because of inclement weather, this seminar talk has been cancelled. Please visit Math Events for a listing of future events in the Department of Mathematics.

 


Title: (L-)principally quasi-Baer modules

Speaker: Gangyong Lee (Chungnam National University, South Korea)

Abstract: The purpose of this talk is to further the study of principally quasi-Baer modules and $\mathfrak{L}$-principally quasi-Baer modules as these properties play an important role in the study of quasi-Baer module. The notion of quasi-Baer modules in a general module theoretic setting was introduced by Rizvi and Roman [4], and then Lee and Rizvi studied the direct sum property for quasi-Baer modules, recently [2]. In addition, many other mathematicians investigated a p.q.-Baer module in a general module theoretic setting for a right p.q.-Baer ring (see [1]) as investigating that for quasi-Baer rings.

First, in this talk, we provide some basic results and a characterization of a principally quasi-Baer (simply, p.q.-Baer) module in terms of its endomorphism ring by using the $pq$-local-retractable property. In addition, we fully characterize when a finite direct sum of arbitrary p.q.-Baer modules is p.q.-Baer.

We obtain characterizations and properties of $\mathfrak{L}$-principally quasi-Baer (simply, $\mathfrak{L}$-p.q.-Baer) modules. Examples which show that the notion of an $\mathfrak{L}$-p.q.-Baer module is distinct from that of a p.q.-Baer module are provided. It is shown that every direct summand of an $\mathfrak{L}$-p.q.-Baer module inherits the property. Furthermore, we obtain that every direct sum of copies of an $\mathfrak{L}$-p.q.-Baer module is an $\mathfrak{L}$-p.q.-Baer module. We provide conditions when ($\mathfrak{L}$-)p.q.-Baer modules become quasi-Baer modules. In particular, if every direct sum of copies of a module $M$ is p.q.-Baer then the module $M$ is a quasi-Baer module.

Works Cited

  1. G.F. Birkenmeier; J.Y. Kim; J.K. Park, Principally quasi-Baer rings, Comm. Algebra, 2001 29(2), 638--660
  2. G. Lee; S.T. Rizvi, Direct sums of quasi-Baer modules, J. Algebra, 2016 456, 76--92
  3. G. Lee, Principally quasi-Baer modules and their generalizations, submitted
  4. S.T. Rizvi; C.S. Roman, Baer and quasi-Baer modules, Comm. Algebra, 2004 32(1), 103--123

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