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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-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...

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.

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.

Simply connected right multipeak algebras and the separation property

Stanisław Kasjan (1999)

Colloquium Mathematicae

Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and ˜ -free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic...

Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let ( Q s g , I s g ) and ( Q g , I g ) be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra K Q s g / ⟨ I s g ⟩ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of K Q g / ⟨ I g ⟩ . As a corollary, we find that g l d i m K Q s g / ⟨ I s g ⟩ < ∞ if and only if g l d i m K Q / ⟨ I ⟩ < ∞ if and only if g l d i m K Q g / ⟨ I g ⟩ < ∞ .

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