ABSTRACT: The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential ...

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 ...

Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of ...

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 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 ...