Introduction. Suppose R and S are local rings and (R, m)→(S, n) is a flat local
homomorphism. Given a finitely generated S-module N, we say N is extended (from R) …

Let M be a matrix whose entries are power series in several variables and determinant det
(M) does not vanish identically. The equation det (M)= 0 defines a hypersurface singularity …

Given a flat local ring homomorphism R → SR→ S and two finitely generated R-modules M
and N, we describe conditions under which the modules\rm Tor^ R _ i (M, N) Tor i R (M, N) …

CONSTRUCTING BIG INDECOMPOSABLE MODULES 1. Introduction A fruitful approach to the
study of a commutative ring is to understand Page 1 PROCEEDINGS OF THE AMERICAN …

arXiv:1805.03587v1 [math.AC] 9 May 2018 Page 1 arXiv:1805.03587v1 [math.AC] 9 May 2018
ALGEBRIZATION OF SOME COMPLETE MODULES MOHSEN ASGHARZADEH ABSTRACT …

arXiv:1302.4151v1 [math.AC] 18 Feb 2013 Page 1 arXiv:1302.4151v1 [math.AC] 18 Feb 2013
ASCENT PROPERTIES FOR DERIVED FUNCTORS SEAN SATHER-WAGSTAFF Abstract …

In the oldest sense, arithmetic is the study of operations on integers: addition, subtraction,
multiplication, and (when defined) division. A somewhat more modern perspective is that …

Consider matrices with entries in a local ring, Mat (m, n; R), suppose a group G acts on Mat
(m, n; R). The matrix A is called G-stable if its orbit GA is open (in the given topology). For the …

This dissertation investigates the interplay between properties of Ext modules and ascent of
module structures along ring homomorphisms. First, we consider a flat local ring …