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When is the idealization R⋉M an 𝒜-ring?
- Source :
-
Journal of Algebra & Its Applications . Dec2020, Vol. 19 Issue 12, pN.PAG-N.PAG. 14p. - Publication Year :
- 2020
-
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 𝒮 𝒜 -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 𝒜 ? (see, Question 4.4(1) in the above mentioned paper). This paper highly contributes to answer such a question. [ABSTRACT FROM AUTHOR]
- Subjects :
- *OPEN-ended questions
*ALGEBRA
*NOETHERIAN rings
*COMMUTATIVE algebra
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 19
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 146343568
- Full Text :
- https://doi.org/10.1142/S0219498820502278