Introduction. All rings are commutative with identity. Let R [X] be a polynomial ring over an
integral domain. Kaplansky (.[3], 102, Exercises 3 and 4) has shown that for a, be R, the …

On the other hand, it is known that, in a local ring Q, if the index of reducibility of an rn-
primary ideal generated by a system of parameters is equal to 1 constantly (ie if every ideal …

Symbolic squares in regular local rings Page 1 Math. Z. 229, 31–44 (1998) c Springer-Verlag
1998 Symbolic squares in regular local rings Craig Huneke, Juergen Ribbe Purdue University …

In a previous note [3] the author gave a short proof for the purity of the branch locus for a
certain class of rings: Assume that R is a normal domain, S its integral closure in a finite …

Let $ f (x) $ be a polynomial in several indeterminates with coefficients in an integral domain
R with quotient field K. We prove that the principal ideal generated by f in the polynomial ring …

All rings in this paper are commutative with unity; we will deal mainly with integral domains.
Let Rhe a ring with total quotient ring K. A fractional ideal/of-R is invertible if II~^= R; …

Introduction. This paper deals (except in? 4) with one-dimensional commutative rings. It
originated with the observation that if A is a complete one-dimensional local domain with an …

Let R be a commutative Noetherian ring and/an ideal in R. There are many natural and
important ways in which the study of the powers of I arises, eg, from the study of Hilbert …

W e say that a ring R is of finitely generated type over a ring S if R is a ring of quotients of a
finitely generated ring over S. W e say that the dimension formula holds for a local integral …

Let R be an integral domain in which all finitely generated ideals are principal. Let M be a
projective R-module. It is well known that if M is finitely generated it is free. By a familiar …