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 ...

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 ...

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 ...

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 ...

An ideal I in the free associative algebra $\kappa \,\langle $X1, ... , X$_{n}\rangle $ over a field k is shown to have a finite Grobner basis if the algebra defined ...