منابع مشابه
Some External Characterizations of SV-Rings and Hereditary Rings
In ring theory, the notion of annihilator is an important tool for studying the structures. Many characterizations and structure theorems can be derived by using this notion. On the other hand, certain classes of rings (e.g., Baer rings and Rickart rings) are defined by considering annihilators ideals. In the present work, we introduce a class of rings which is close to the class of Rickart rin...
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A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and P-coherent rings with property (P).
متن کاملCharacterizations of Semiperfect and Perfect Rings(∗)
We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective coves are adapted from Azumaya’s generalized projective covers.
متن کاملCharacterizations of Krull Rings with Zero Divisors
We show that a ring is a Krull ring if and only if every nonzero regular prime ideal contains a t-invertible prime ideal if and only if every proper regular principal ideal is quasi-equal to a product of prime ideals.
متن کاملSome Characterizations of Domination
We show that a cocycle has a dominated splitting if and only if there is a uniform exponential gap between singular values of its iterates. Then we consider sets Σ in GL(d, R) with the property that any cocycle with values in Σ has a dominated splitting. We characterize these sets in terms of existence of invariant multicones, thus extending a 2-dimensional result by Avila, Bochi, and Yoccoz. W...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2009
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870802502761