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.

World Scientific's newly published book A Non-Hausdorff Completion: The Abelian Category of C-complete Left Modules over a Topological Ring, introduces an entirely new invariant in commutative (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 ...

Commutative algebra and graph theory are two vibrant areas of mathematics that have grown increasingly interrelated. At this interface, algebraic methods are applied to study combinatorial structures, ...

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 project, we attempt to reformulate various notions from classical commutative algebra (such as flatness, regularity, smoothness, etc.) in an entirely categorical manner, so as to be able to ...

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 ...

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 ...

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 ...