In this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module.With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime element in multiplication lattice modules.
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let be a commutative ring with a nonzero identity and a proper ideal of . The proper ideal is said to be a weakly strongly quasi-primary ideal if whenever for some , then or Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional...
Recently, motivated by Anderson, Dumitrescu’s -finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of -coherent rings, which is the -version of coherent rings. Let be a commutative ring with unity graded by an arbitrary commutative monoid , and a multiplicatively closed subset of nonzero homogeneous elements of . We define to be graded--coherent ring if every finitely generated homogeneous ideal of is -finitely presented. The purpose of this paper is to give the graded...
This paper deals with the rings which satisfy condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings and the...
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