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Rings Characterized by Direct Sums of CS Modules

Er, Noyan Fevzi

Abstract Details

2003, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).

A Module M is called a CS module if every submodule of M is essential in a direct summand of M. In this dissertation certain classes of rings characterized by direct sums of CS modules are considered. It is proved that for a ring R for which either soc(RR) or E(RR) is finitely generated, the following hold: (i) R is a right Artinian ring and all uniform right R-modules are Σ-quasi-injective iff for every CS right R-module M, M(N) is CS, and; (ii) R is a right Artinian ring and all uniform right R-modules have composition length at most two iff the direct sum of any two CS right R-modules is again CS. Partial answers are obtained to a question of Huynh whether a semilocal ring or a ring with finite right uniform dimension that is right countably Σ-CS is right Σ-CS. The results obtained in this dissertation yield, in particular, new characterizations of QF-rings. These results extend previously known results due to several authors such as Clark, Dung, Gómez Pardo, Guil Asensio, Huynh, Jain, López-Permouth, Müller, Oshiro and others.

D.V. Huynh (Advisor)
58 p.

Recommended Citations

Citations

  • Er, N. F. (2003). Rings Characterized by Direct Sums of CS Modules [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1069450867

    APA Style (7th edition)

  • Er, Noyan. Rings Characterized by Direct Sums of CS Modules. 2003. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1069450867.

    MLA Style (8th edition)

  • Er, Noyan. "Rings Characterized by Direct Sums of CS Modules." Doctoral dissertation, Ohio University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1069450867

    Chicago Manual of Style (17th edition)