On Dual Baer Modules

Abstract

Abstract. In this paper we introduce T -non-cosingular modules, dual Baer modules and K-modules. We prove that a module M is lifting and T -non-cosingular if and only if it is a dual Baer and K-module. Rings for which all modules are dual Baer are precisely determined. We also give a necessary condition for a finite direct sum of dual Baer modules to be dual Baer.2000 Mathematics Subject Classification. 16D10, 16D80, 16E60.

Some results on relative dual Baer property

“…According to [10], a module M is called a Baer module if for every left ideal I of End R (M ), ∩ φ∈I Kerφ is a direct summand of M . This notion was recently dualized by Keskin Tütüncü-Tribak in [14]. A module M is said to be dual Baer if for every right ideal Tayyebeh Amouzegar; Department of Mathematics, Quchan University of Advanced Technology, Quchan, Iran (email: t.amoozegar@yahoo.com).…”

“…I of S = End R (M ), φ∈I Imφ is a direct summand of M . Equivalently, for every nonempty subset A of S, φ∈A Imφ is a direct summand of M (see [14,Theorem 2…”

Rickart and Dual Rickart Objects in Abelian Categories: Transfer via Functors

“…Secondly, our concepts generalize to the level of abelian categories Rickart and dual Rickart modules in the sense of Lee, Rizvi and Roman [18,19,20], and in particular, Baer and dual Baer modules studied by Rizvi and Roman [25,26] and Keskin Tütüncü, Smith, Toksoy and Tribak [16,17]. A unified approach of Baer and dual Baer modules via Baer-Galois connections was given by Olteanu in [24], following the approach by Crivei from [5].…”

Some results on T-noncosingular modules

“…It was shown in [21] that every dual Baer module is T -noncosingular and that every T -noncosingular lifting module is dual Baer. We note also that dual Rickart modules were introduced and studied by Lee et al in 2011 [12] and it is easy to see that every dual Rickart module is T -noncosingular.…”