منابع مشابه
Some Small-Centralizer Properties for Rings
We characterize rings R in which certain elements x have the property that CR(x) (resp. the set of zero divisors in CR(x)) is finite. We also explore the consequences of an assumption that certain x satisfy CR(x) = 〈x〉.
متن کاملHomological Characterizations of Rings with Property (P)
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 کاملOn Polynomial Rings with a Goldbach Property
David Hayes observed in 1965 that when R = Z, every element of R[T ] of degree n ≥ 1 is a sum of two irreducibles in R[T ] of degree n. We show that this result continues to hold for any Noetherian domain R with infinitely many maximal ideals. It appears that David Hayes [5] was the first to observe the following polynomial analogue of the celebrated Goldbach conjecture: If R = Z, then (?) ever...
متن کاملDescent of Semidualizing Complexes for Rings with the Approximation Property
Let R be a commutative noetherian local ring with completion b R. When R has the approximation property, we prove an approximation result for complexes with finitely generated homology. This is used to investigate descent of semidualizing complexes from b R to R. We show that, if R has the approximation property, then there is a bijective correspondence between semidualizing b R-complexes and s...
متن کاملThe Cohen - Macaulay Property of Invariant Rings
If V is a faithful module for a nite group G over a eld of characteristic p > 0, then the ring of invariants need not be Cohen-Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen-Macaulayness of the invariant ring. Let R = S(V) be the polynomial ring on which G acts. Then the main result can be stated as follow: If H r (G; R) 6 = 0 fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90163-9