#### 64 Citations

Factorization in general rings and strictly cyclic modules.

- Mathematics
- 1969

The problem of factorization in noncommutative rings first arose in analysis, where the solution of a linear differential equation was reduced to the factorization of a linear differential operator… Expand

The syzygy theorem and the Weak Lefschetz property

- Mathematics
- 2011

This thesis consists of two research topics in commutative algebra.
In the first chapter, a comprehensive analysis is given of the Weak Lefschetz property in the case of ideals generated by powers… Expand

On p-radical descent of higher exponent

- Mathematics
- 1981

In the paper [8], P. Samuel has developed the theory of ^-radical descent of exponent one by making use of logarithmic derivatives. In this article we shall give a generalization of his theory to the… Expand

On unique factorization domains

- Mathematics
- 1961

where u is a unit and p1, p2,. . . ,pk are primes in R. Note that the factorization is essentially unique (by the same argument used to prove uniqueness of factorization in PIDs). Note also that if R… Expand

The biregular cancellation problem

- Mathematics
- 1987

The main purpose of this paper is to study the relationship of the above two problems. We apply the results of the birational cancellation problem [17, 4 and 13] to investigate the biregular… Expand

Atomic rings and the ascending chain condition for principal ideals

- Mathematics
- 1974

Let R be a commutative ring. We say that R satisfies the ascending chain condition for principal ideals , or that R has property ( M ), if each ascending sequence ( a 1 ) ⊆ ( a 2 ) ⊆ … of principal… Expand

FACTORIAL AFFINE Gα-VARIETIES ISOMORPHIC TO HYPERSURFACES OF DANIELEWSKI TYPE

- Mathematics
- 2020

Let k be an algebraically closed field of characteristic zero and B a factorial affine k-domain equipped with a locally nilpotent derivation δ. We investigate B when there exists an element z ∈ B… Expand

AFFINE THREEFOLDS WITH A$$ \mathbb{A} $$2-FIBRATIONS

- Mathematics
- 2016

An affine threefold containing an A$$ \mathbb{A} $$2-cylinder is studied. The existence of A$$ \mathbb{A} $$2-cylinders is almost equivalent to the existence of mutually commuting, independent… Expand

What v-coprimality can do for you

- Mathematics
- 2006

LetD be an integral domain with quotient fieldK. Two elements x, y ∈ D\{0} are said to be v-coprime if xD ∩ yD = xyD. A saturated multiplicative set S ⊆ D\{0} is a splitting set of D if every x ∈… Expand

Conformally Osserman manifolds of dimension 16 and a Weyl–Schouten theorem for rank-one symmetric spaces

- Mathematics
- 2012

A Riemannian manifold is called Osserman (conformally Osserman, respectively), if the eigenvalues of the Jacobi operator of its curvature tensor (Weyl tensor, respectively) are constant on the unit… Expand