Representation-finite algebras and multiplicative bases.
Restricted Regular Rings.
Rigid monomial algebras.
Ringe mit verallgemeinerter Kupischreihe.
Rings consisting entirely of certain elements
We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; ; where is a Boolean ring; local ring with nil Jacobson radical; or ; or the ring of a Morita context with zero pairings where the underlying rings are or .
Rings decomposed into direct sums of J-rings and nil rings.
Rings generalized by tripotents and nilpotents
We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).
Rings which are semilattices of archimedean semigroups.
Rings whose Elements are Quasi-Regular or Regular
Rings whose nonsingular right modules are -projective
A right -module is called -projective provided that it is projective relative to the right -module . This paper deals with the rings whose all nonsingular right modules are -projective. For a right nonsingular ring , we prove that is of finite Goldie rank and all nonsingular right -modules are -projective if and only if is right finitely - and flat right -modules are -projective. Then, -projectivity of the class of nonsingular injective right modules is also considered. Over right...
Rings with many idempotents.
-pure submodules.
-weakly regular group rings
In this note we obtain a necessary and sufficient condition for a ring to be -weakly regular (i) When is a ring with identity and without divisors of zero (ii) When is a ring without divisors of zero. Further it is proved in a -weakly regular ring with identity and without units every element is a zero divisor.
Self-equivalences of the derived category of Brauer tree algebras with exceptional vertex.
Self-injective Von Neumann regular subrings and a theorem of Pere Menal.
This paper owes its origins to Pere Menal and his work on Von Neumann Regular (= VNR) rings, especially his work listed in the bibliography on when the tensor product K = A ⊗K B of two algebras over a field k are right self-injective (= SI) or VNR. Pere showed that then A and B both enjoy the same property, SI or VNR, and furthermore that either A and B are algebraic algebras over k (see [M]). This is connected with a lemma in the proof of the Hilbert Nullstellensatz, namely a finite ring extension...
Semiprime SF-rings whose essential left ideals are two-sided.
Semirings embedded in a completely regular semiring
Recently, we have shown that a semiring is completely regular if and only if is a union of skew-rings. In this paper we show that a semiring satisfying can be embedded in a completely regular semiring if and only if is additive separative.
Semisimple ring spectra.
Semisimplicity and global dimension of a finite von Neumann algebra
We prove that a finite von Neumann algebra is semisimple if the algebra of affiliated operators of is semisimple. When is not semisimple, we give the upper and lower bounds for the global dimensions of and This last result requires the use of the Continuum Hypothesis.
SGn of Orders and Group-Rings.