Rational extensions of modules

Storrer, Hans H.

doi:10.2140/pjm.1971.38.785

Cited by 10 publications

(2 citation statements)

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“…Finally, it is important to remember that, as we noted earlier, there are relatively few references that have been concerned with studying rational submodules such as [15] and [18][19][20][21][22], which is what motivated us to carry out this study.…”

Section: Corollary 222mentioning

confidence: 99%

P-Rational Submodules

Baher,

Ahmed

2024

Iraqi Journal of Science

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A submodule N is called rational in M if ( , E(M))=0, where E(M) is the an injective hull of M. Rational submodules have been studied and discussed by many authors such as H.H. Storrer, H. Khabazian, E. Ghashghaei, A. Hajikarimi, M.S. Abbas and M.S. Nayef. The main objective of this paper is to give a new class of submodules named P-rational submodules. This class is contained properly in the class of rational submodules. Several properties of this concept are introduced. The relationships between this class of submodules and some other related concepts are discussed such as essential and quasi-invertible submodules. Other characterizations of the P-rational submodule analogous to those which is known in the concept of the rational submodule are given.

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Section: Corollary 222mentioning

confidence: 99%

P-Rational Submodules

Baher,

Ahmed

2024

Iraqi Journal of Science

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“…This paper can be viewed as a continuation of the authors' previous investigations of preradicals [l] - [6] and is devoted to the methods of constructing preradicals from given fragments which seems to be useful in several directions, see e.g. [7] - [9]. It is shown that choosing arbitrary submodules of some modules gives rise to a preradical.…”

Section: Introductionmentioning

confidence: 99%