Bouchiba, S. and El-Arabi, M. and Khaloui, M. (2019) When is the idealization R ⋉ M an A-ring? Journal of Algebra and its Applications.

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Abstract

We present an answer to a problem raised by Anderson and Chun in D. D. Anderson and S. Chun, Annihilator conditions on modules over commutative rings, J. Algebra Appl. 16(7) (2017) 1750143 on characterizing when the idealization R ⋉ M of a ring R on an R-module M is an A-ring (respectively, an SA-ring) in terms of module-theoretic properties of R and M. Also, we are concerned with an open question asked by these two authors which reads the following: What modules over a given ring R are homomorphic images of modules satisfying the strong Property ? (see, Question 4.4(1) in the above mentioned paper). This paper highly contributes to answer such a question. © 2020 World Scientific Publishing Company.

Item Type:	Article
Subjects:	Mathematics
Divisions:	SCIENTIFIC PRODUCTION > Mathematics
Depositing User:	Administrateur Eprints Administrateur Eprints
Last Modified:	31 Jan 2020 15:48
URI:	http://eprints.umi.ac.ma/id/eprint/3868

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