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 …

Let R be a commutative ring and K be a submodule of Rm, and let I be the first nonzero
Fitting ideal of the module M= Rm/K. A lemma of Lipman asserts that if R is quasilocal and I …

This paper supplements work of Ohm-Rush. A question which was raised by them is
whether $ R [X]/I $ is a flat R-module implies I is locally finitely generated at primes of $ R [X] …

If A is a commutative ring with identity and B is a unitary A-algebra, B is locally polynomial
over A provided that for every prime p of A, ${B_p}= B {\otimes _A}{A_p} $ is a polynomial …

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 …

Let $ R $ be a commutative ring with identity $1\ne 0$ and let $ A $ be a nonzero ideal of $
R $. A problem of current interest is to relate the notions of “projective ideal",“flat ideal” and …

Some well-known theorems indicate that certain ideal-theoretic structure properties of a
commutative ring R are determined by the set of prime ideals of R. For example, R is …

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 …

Unlike the situation when dealing with integral domains, it is not always the case that the
polynomial ring $ R\left [X\right] $ is integrally closed when $ R $ is an integrally closed …

Thus, for x EI we get and the xi's generate I. We show this to be the case for J. Notice ICJ; if J
is not A, let M be a maximal ideal containing it. By hypothesis M is not a minimal prime ideal …