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On the K-theory of the C * -algebra generated by the left regular representation of an Ore semigroup

Joachim Cuntz, Siegfried Echterhoff, Xin Li (2015)

Journal of the European Mathematical Society

We compute the K -theory of C * -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the K -theory of these semigroup C * -algebras in terms of the K -theory for the reduced group C * -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

On the lattice of congruences on inverse semirings

Anwesha Bhuniya, Anjan Kumar Bhuniya (2008)

Discussiones Mathematicae - General Algebra and Applications

Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences ρ m i n , ρ m a x , ρ m i n and ρ m a x on S and showed that ρ θ = [ ρ m i n , ρ m a x ] and ρ κ = [ ρ m i n , ρ m a x ] . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if ρ m a x is a distributive lattice congruence and ρ m a x is a skew-ring congruence on S. If η (σ) is the least distributive...

On the lattices of quasivarieties of differential groupoids

Aleksandr Kravchenko (2008)

Commentationes Mathematicae Universitatis Carolinae

The main result of Romanowska A., Roszkowska B., On some groupoid modes, Demonstratio Math. 20 (1987), no. 1–2, 277–290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is 𝒬 -universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties....

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