If k is a field, k [x] is a principal ideal domain and the ideal structure of k [x] is well
understood. For example, a nonzero ideal is prime if and only if its generator is irreducible. If …

1. Introduction. The concept of prime ideal has played an important role in the theory of
commutative rings, but has not been used so extensively in the study of noncommutative …

This paper is concerned with the ideal theory of a commutative ring R. We say R has
Property (α) if each primary ideal in R is a power of its (prime) radical; R is said to have …

Let $ R $ be a commutative ring with identity, let $ X $ be an indeterminate, and let $ I $ be
an ideal of the polynomial ring $ R [X] $. Let $\min I $ denote the set of elements of $ I $ of …

All rings are Noetherian, commutative, with 1, and contain a field. We define the tight closure
of an ideal in characteristic p and for algebras essentially of finite type over a field, and use it …

The main result of this paper is the explicit determination of the core of integrally closed
ideals in 2-dimensional regular local rings. The core of an ideal I in a ring R was introduced …

1. Introduction. Throughout this paper all rings are assumed to be integral domains with
unity. If F is an integral domain F* will denote the set of nonzero elements of F. An integral …

Some theorems concerning the prime divisors of a principal ideal in a Krull domain are
generalized to results on the prime divisors of the integral closure of a principal ideal in the …

Let R be a domain with quotient field K, and let I be an ideal of R. We say that I is powerful
(strongly primary) if whenever and, we have or (or for some). We show that an ideal with …

It is our purpose in this paper to investigate the relationship between two classes of ideals in
regular local rings R: prime ideals P such that R/P is factorial, and prime ideals Q which are …