DSpace-CRIS at TU Wienhttps://repositum.tuwien.atThe reposiTUm digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 29 Nov 2022 18:49:43 GMT2022-11-29T18:49:43Z5031A note on homomorphisms between products of algebrashttp://hdl.handle.net/20.500.12708/564Title: A note on homomorphisms between products of algebras
Authors: Chajda, Ivan; Goldstern, Martin; Länger, Helmut
Abstract: Let K be a congruence distributive variety and call an algebra hereditarily directly irreducible (HDI) if every of its subalgebras is directly irreducible. It is shown that every homomorphism from a finite direct product of arbitrary algebras from K to an HDI algebra from K is essentially unary. Hence, every homomorphism from a finite direct product of algebras Ai (i∈I) from K to an arbitrary direct product of HDI algebras Cj (j∈J) from K can be expressed as a product of homomorphisms from Aσ(j) to Cj for a certain mapping σ from J to I. A homomorphism from an infinite direct product of elements of K to an HDI algebra will in general not be essentially unary, but will always factor through a suitable ultraproduct.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/5642018-01-01T00:00:00ZThe lattice of subspaces of a vector space over a finite fieldhttp://hdl.handle.net/20.500.12708/708Title: The lattice of subspaces of a vector space over a finite field
Authors: Chajda, Ivan; Länger, Helmut
Wed, 01 May 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7082019-05-01T00:00:00ZLeft residuated operators induced by posets with a unary operationhttp://hdl.handle.net/20.500.12708/739Title: Left residuated operators induced by posets with a unary operation
Authors: Chajda, Ivan; Länger, Helmut
Abstract: The concept of operator left residuation has been introduced by the authors in their previous paper (Chajda and Länger in Asian Eur J Math 11:1850097, 2018). Modifications of so-called quantum structures, in particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and Boolean posets are investigated here in order to show that they are operator left residuated or even operator residuated. In fact, they satisfy more general sufficient conditions for operator residuation assumed for bounded posets equipped with a unary operation. It is shown that these conditions may be also necessary if a generalized version using subsets instead of single elements is considered. The above-listed posets can serve as an algebraic semantics for the logic of quantum mechanics in a broad sense. Moreover, our approach shows connections to substructural logics via the considered residuation.
Fri, 01 Nov 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/7392019-11-01T00:00:00Z