Conditioned Cancellation Modules

A Note on Cancellation of Reflexive Modules

By the Quillen-Suslin theorem [Qui76, Sus76], we know that projective modules over a polynomial ring over a field are free. One way of saying this is, that if two projective modules of the same rank are stably isomorphic, then they are isomorphic. That, projective modules of given rank over polynomial rings are stably isomorphic was well known at the time Quillen and Suslin proved their theorem...

Direct Sum Cancellation for Modules over One-dimensional Rings

Let R be a one-dimensional Noetherian domain with finite normalization R. In the eighties the second-named author and S. Wiegand developed a mechanism for studying the cancellation problem for finitely generated torsion-free R-modules. The key idea, described in [Wie84] and [WW87], is to represent a given torsion-free module M as a pullback: M −→ RM ↓ ↓ M/fM −→ RM/fM ∗This research was initiate...

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

SEMI-RADICALS OF SUB MODULES IN MODULES

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Cancellation theorem