Quasi-decompositions and quasidirect products of Hilbert algebras
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Jānis Cīrulis
Abstract
A quasi-decomposition of a Hilbert algebra A is a pair (C, D) of its subalgebras such that (i) every element a ∈ A is a meet c ∧ d with c ∈ C, d ∈ D, where c and d are compatible (i.e., c → d = c → (c ∧ d)), and (ii) d → c = c (then c is uniquely defined). Quasi-decompositions are intimately related to the so-called triple construction of Hilbert algebras, which we reinterpret as a construction of quasidirect products. We show that it can be viewed as a generalization of the semidirect product construction, that quasidirect products has a certain universal property and that they can be characterised in terms of short exact sequences. We also discuss four classes of Hilbert algebras and give for each of them conditions on a quasi-decomposition of an arbitrary Hilbert algebra A under which A belongs to this class.
(Communicated by Anatolij Dvurečenskij)
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© 2021 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular Papers
- Quasi-decompositions and quasidirect products of Hilbert algebras
- Residuation in finite posets
- On a problem in the theory of polynomials
- Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
- Mapping properties of the Bergman projections on elementary Reinhardt domains
- Lemniscate-like constants and infinite series
- On the Oscillation of second order nonlinear neutral delay differential equations
- Oscillation theorems for certain second-order nonlinear retarded difference equations
- De la Vallée Poussin inequality for impulsive differential equations
- Hs-Boundedness of a class of Fourier Integral Operators
- Dynamical behavior of a P-dimensional system of nonlinear difference equations
- Some inequalities for exponentially convex functions on time scales
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- Simulations of nonlinear parabolic PDEs with forcing function without linearization
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- A relationship between the category of chain MV-algebras and a subcategory of abelian groups
Articles in the same Issue
- Regular Papers
- Quasi-decompositions and quasidirect products of Hilbert algebras
- Residuation in finite posets
- On a problem in the theory of polynomials
- Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
- Mapping properties of the Bergman projections on elementary Reinhardt domains
- Lemniscate-like constants and infinite series
- On the Oscillation of second order nonlinear neutral delay differential equations
- Oscillation theorems for certain second-order nonlinear retarded difference equations
- De la Vallée Poussin inequality for impulsive differential equations
- Hs-Boundedness of a class of Fourier Integral Operators
- Dynamical behavior of a P-dimensional system of nonlinear difference equations
- Some inequalities for exponentially convex functions on time scales
- Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
- The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
- A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
- Simulations of nonlinear parabolic PDEs with forcing function without linearization
- An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
- A relationship between the category of chain MV-algebras and a subcategory of abelian groups
