Commutative algebra and algebraic geometry form a deeply interwoven field that investigates the structure of polynomial rings, their ideals, and the geometric objects defined by these algebraic sets.

This course gives an introduction to commutative rings and their modules. We study concepts such as localization, decomposition of modules, chain conditions for rings and modules, and dimension theory ...

There was an error while loading. Please reload this page. This is the homepage for my Commutative Algebra book. It is meant to be the first of two volumes, the ...

ABSTRACT: Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and ...

ABSTRACT: This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The ...

A more thorough introduction to the topics covered in this section can be found in the *Elementary Algebra* chapter, Foundations. of AdditionIfa,b,andcare real numbers, then(a+b)+c=a+(b+c). of ...

Introduction to commutative algebra. Noetherian rings and modules. Local algebra and primary decomposition. The course may also include subjects from non-commutative algebra such as group and ...

In this course you will study structural theorems for commutative rings, with applications in algebraic geometry, algebraic number theory, and complex analysis. To construct and study new commutative ...

Now for rather different reasons I’m returning to it. But commutative separable algebras are also interesting. They are important in Grothendieck’s approach to Galois theory. So, I want to understand ...