http://dspace.nbuv.gov.ua:80/handle/123456789/150343 2026-04-18T12:14:51Z http://dspace.nbuv.gov.ua:80/handle/123456789/157389 The generalized path algebras over standardly stratified algebras Wang, S. In this note, it is proved that the generalized path algebras over standardly stratified algebras are also standardly stratified, and the generalized path algebras over quasi-hereditary algebras are also quasi-hereditary. The ∆−good module categories over these big quasi-hereditary algebras are determined in terms of those of the given algebras. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157386 Arithmetic properties of exceptional lattice paths Rump, W. For a fixed real number ρ > 0, let L be an affine line of slope ρ ⁻¹ in R ² . We show that the closest approximation of L by a path P in Z ² is unique, except in one case, up to integral translation. We study this exceptional case. For irrational ρ, the projection of P to L yields two quasicrystallographic tilings in the sense of Lunnon and Pleasants [5]. If ρ satisfies an equation x ² = mx + 1 with m ∈ Z, both quasicrystals are mapped to each other by a substitution rule. For rational ρ, we characterize the periodic parts of P by geometric and arithmetic properties, and exhibit a relationship to the hereditary algebras Hρ(K) over a field K introduced in a recent proof of a conjecture of Ro˘ıter. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157383 Absolutely ubiquitous groups Ivanov, A.; Majcher, K. We characterise absolutely ubiquitous groups in the class of model complete ω-categorical groups. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157379 On 𝔉-radicals of finite π-soluble groups Guo, W.; Xi Liu; Baojun Li In this paper, we prove that for every local πsaturated Fitting class 𝔉 with char(𝔉) = P, the F-radical of every finite π-soluble groups G has the property: CG(G𝔉 ) ⊆ G𝔉 . From this, some well known results are followed and some new results are obtained. 2006-01-01T00:00:00Z