A net (xγ)γ∈Γ in a locally solid Riesz space (X,τ) is said to be unbounded τ-convergent x if |xγ−x|∧u⟶τ0 for all u∈X+. We recall that there linear topology uτ on X such τ-convergence coincides with uτ-convergence. It turns out characterised as the weakest which τ order bounded subsets. this motivation we introduce, uniform lattice (L,u), uniformity u⁎ L u subsets of L. shown induced by (X,τ), t...

We introduce the notions of τ -exceptional and signed sequences for any finite dimensional algebra. prove that a fixed algebra rank n , positive integer t ≤ there is bijection between set length (basic) ordered support -rigid objects with indecomposable direct summands. If hereditary, our coincide exceptional sequences. The latter were recently introduced by Igusa Todorov, who constructed simil...

We study the elliptic algebras Qn,k(E,τ) introduced by Feigin and Odesskii as a generalization of Sklyanin algebras. They form family quadratic parametrized coprime integers n>k≥1, an curve E, point τ∈E. consider compare several different definitions provide proofs various statements about them made Odesskii. For example, we show that Qn,k(E,0), Qn,n−1(E,τ) are polynomial rings on n variables. ...