Geodesic
Module decompositions by images of fully invariant submodules
Filomat, Tome 35 (2021) no. 11, p. 3679

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DOI

Let R be a ring with identity, M be a right R-module and F be a fully invariant submodule of M. The concept of an F-inverse split module M has been investigated recently. In this paper, we approach to this concept with a different perspective, that is, we deal with a notion of an F-image split module M, and study various properties and obtain some characterizations of this kind of modules. By means of F-image split modules M, we focus on modules M in which fully invariant submodules F are dual Rickart direct summands. In this way, we contribute to the notion of a T-dual Rickart module M by considering Z 2 (M) as the fully invariant submodule F of M. We also deal with a notion of relatively image splitness to investigate direct sums of image split modules. Some applications of image split modules to rings are given
DOI : 10.2298/FIL2111679P
Classification : 16D70, 16D10, 16D40, 16D80
Keywords: Dual Rickart module, image split module, fully invariant submodule, direct summand 
Tugce Pekacar Calci; Burcu Ungor; Abdullah Harmanci. Module decompositions by images of fully invariant submodules. Filomat, Tome 35 (2021) no. 11, p. 3679 . doi: 10.2298/FIL2111679P
@article{10_2298_FIL2111679P,
     author = {Tugce Pekacar Calci and Burcu Ungor and Abdullah Harmanci},
     title = {Module decompositions by images of fully invariant submodules},
     journal = {Filomat},
     pages = {3679 },
     year = {2021},
     volume = {35},
     number = {11},
     doi = {10.2298/FIL2111679P},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2111679P/}
}
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