Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms

Pure Subrings of Regular Rings Are Pseudo-rational

We prove a generalization of the Hochster-Roberts-Boutot-Kawamata Theorem conjectured in [1]: let R → S be a pure homomorphism of equicharacteristic zero Noetherian local rings. If S is regular, then R is pseudo-rational, and if R is moreover Q-Gorenstein, then it is pseudo-log-terminal.

Fixed Subrings of Noetherian Graded Regular Rings

Rings of invariants can have nice homological properties even if they do not have finite global dimension. Watanabe’s Theorem [W] gives conditions when the fixed subring of a commutative ring under the action of a finite group is a Gorenstein ring. The Gorenstein condition was extended to noncommutative rings by a condition explored by Idun Reiten in the 1970s, called k-Gorenstein in [FGR]. Thi...

Endomorphism Rings of Modules over Prime Rings

Endomorphism rings of modules appear as the center of a ring, as the fix ring of a ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain ∗-prime modules have a prime endomorphism ring. Several conditions are presented that guarantee the primeness of the endomorphism ring. The contours of a possible example of a ∗-prime module who...

Endomorphism rings of bimodules

Endomorphism Rings in Cryptography

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