Commutative Algebra Seminar

Title

Using free constructions to answer questions in algebra

Abstract

It is not difficult to construct a commutative ring R with R isomorphic to R[x]. But is it possible to have R isomorphic to R[x,y] and yet R not isomorphic to R[x]?

Similarly, it is easy to show that if R is a commutative ring, and M,N are two right R-modules with the ascending chain condition on cyclic submodules, then M direct sum N has the same property. Does the same result hold for the ascending chain condition on finitely generated submodules?

We discuss approaches to these, and other, questions, using free constructions.