ALC Seminar | Speaker: Elena Caviglia (Stellenbosch University, South Africa)
Title: On extensions of Cohen Structure Theorem
Abstract: For which rings R there exists a maximal ideal M of R such that the canonical projection from R to the quotient R/M has a section, so that R/M is isomorphic to a field contained in R? Cohen Structure Theorem ensures that this is true for any equicharacteristic complete local Noetherian commutative ring. In this talk, we will present two equivalent characterizations of this property and use them to exhibit two large classes of rings that satisfy it. Moreover, we will provide several examples (not necessarily local or complete local), as well as methods to construct new examples. The talk is based on a joint work with Amartya Goswami and Luca Mesiti.