EuDML | Browse

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; $ℤ_{3} \oplus ℤ_{3}$ ; $ℤ_{3} \oplus B$ where $B$ is a Boolean ring; local ring with nil Jacobson radical; $M_{2} (ℤ_{2})$ or $M_{2} (ℤ_{3})$ ; or the ring of a Morita context with zero pairings where the underlying rings are $ℤ_{2}$ or $ℤ_{3}$ .

Rings decomposed into direct sums of J-rings and nil rings.

Tominaga, Hisao (1985)

International Journal of Mathematics and Mathematical Sciences

Rings generalized by tripotents and nilpotents

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2022)

Czechoslovak Mathematical Journal

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.

M.S. Putcha (1981)

Semigroup forum

Rings whose Elements are Quasi-Regular or Regular

W. KEITH NICHOLSON (1973)

Aequationes mathematicae

Rings whose nonsingular right modules are $R$ -projective

Yusuf Alagöz, Sinem Benli, Engin Büyükaşık (2021)

Commentationes Mathematicae Universitatis Carolinae

A right $R$ -module $M$ is called $R$ -projective provided that it is projective relative to the right $R$ -module $R_{R}$ . This paper deals with the rings whose all nonsingular right modules are $R$ -projective. For a right nonsingular ring $R$ , we prove that $R_{R}$ is of finite Goldie rank and all nonsingular right $R$ -modules are $R$ -projective if and only if $R$ is right finitely $Σ$ - $C S$ and flat right $R$ -modules are $R$ -projective. Then, $R$ -projectivity of the class of nonsingular injective right modules is also considered. Over right...

Rings with many idempotents.

Chen, Huanyin (1999)

International Journal of Mathematics and Mathematical Sciences

$s$ -pure submodules.

Crivei, Iuliu (2005)

International Journal of Mathematics and Mathematical Sciences

$s$ -weakly regular group rings

W. B. Vasantha Kandasamy (1993)

Archivum Mathematicum

In this note we obtain a necessary and sufficient condition for a ring to be $s$ -weakly regular (i) When $R$ is a ring with identity and without divisors of zero (ii) When $R$ is a ring without divisors of zero. Further it is proved in a $s$ -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.

Zimmermann, Alexander (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Self-injective Von Neumann regular subrings and a theorem of Pere Menal.

Carl Faith (1992)

Publicacions Matemàtiques

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.

Zhang, Jule, Du, Xianneng (1994)

International Journal of Mathematics and Mathematical Sciences

Semirings embedded in a completely regular semiring

M. K. Sen, S. K. Maity (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Recently, we have shown that a semiring $S$ is completely regular if and only if $S$ is a union of skew-rings. In this paper we show that a semiring $S$ satisfying $a^{2} = n a$ can be embedded in a completely regular semiring if and only if $S$ is additive separative.

Semisimple ring spectra.

Hovey, Mark, Lockridge, Keir (2009)

The New York Journal of Mathematics [electronic only]

Semisimplicity and global dimension of a finite von Neumann algebra

Lia Vaš (2007)

Mathematica Bohemica

We prove that a finite von Neumann algebra $𝒜$ is semisimple if the algebra of affiliated operators $𝒰$ of $𝒜$ is semisimple. When $𝒜$ is not semisimple, we give the upper and lower bounds for the global dimensions of $𝒜$ and $𝒰 .$ This last result requires the use of the Continuum Hypothesis.

SGn of Orders and Group-Rings.

Aderemi O. Kuku (1979)

Mathematische Zeitschrift

Currently displaying 481 – 500 of 677

Previous Page 25 Next