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 ...

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 ...

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 ...

Commutative algebra formalized in Coq using SSReflect/MathComp & packed classes. This repository is part of the Coq/SSReflect algebraic geometry project. All rings here are commutative and has 1, as ...

ABSTRACT: The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear ...

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 ...