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- Title
ON (A)-RINGS AND STRONG (A)-RINGS ISSUED FROM AMALGAMATIONS.
- Authors
MAHDOU, NAJIB; MOUTUI, MOUTU ABDOU SALAM
- Abstract
A ring R has the (A)-property (resp., strong (A)-property) if every finitely generated ideal of R consisting entirely of zero divisors (resp., every finitely generated ideal of R generated by a finite number of zero-divisors elements of R) has a nonzero annihilator. The class of commutative rings with property (A) is quite large; for example, Noetherian rings, rings whose prime ideals are maximal, the polynomial ring R[x] and rings whose total ring of quotients are von Neumann regular. Let f : A → B be a ring homomorphism and J be an ideal of B. In this paper, we investigate when the (A)-property and strong (A)-property are satisfied by the amalgamation of rings denoted by A ⋈f J, introduced by D'Anna, Finocchiaro and Fontana in [3]. Our aim is to construct new original classes of (A)-rings that are not strong (A)-rings, (A)-rings that are not Noetherian and (A)-rings whose total ring of quotients are not Von Neumann regular rings.
- Subjects
FINITE rings; RING theory; DIVISION rings; HOMOMORPHISMS; VON Neumann regular rings; ASSOCIATIVE rings
- Publication
Studia Scientiarum Mathematicarum Hungarica, 2018, Vol 55, Issue 2, p270
- ISSN
0081-6906
- Publication type
Article
- DOI
10.1556/012.2018.55.2.1397