Year: 1978
Type: article
Abstract: Generalized Post algebras were investigated by many authors (see [2], [3], [2], [10] and [12J).1'he known generalizations usually consist in a weakening of the conditions concerning the chain of constants.In this paper the generalization takes another direction -instead of distributive lattices with 0 and 1, what we call d-posets are considered.In a d-poset one only assumes that least upper bounds exiat for disjoint elements and one weakens the condition of distributivity.Assuming that a chain of constants exists in a d-poset and imposing conditions analogous to those of Post algebras, one defines the Post posets and studies their basic properties, 'ihe Boolean center of a Post algebra is replaced in the Post poset by a Boolean orthoposet.Then a Post poset is a generalization of a Post algebra on one hand of a Boolean orthoposet on the other.Post algebras can be characterized as Post posets in which any two complemented elements have a greatest lower bound.Theorems about the uniqueness of the chain of constants, uniqueness of monotone representation also hold in the larger class of Post posets.An example of a Post poset which is not a Post algebra is given.In this paper the usual lattice notation is employed.The least upper bound (l.u.b) of x and y is denoted by x v y and the greatest lower bound (g.l.b.) by x A y, or more briefly by xy.The symbols V X. and /\ x. deiel 1 iel
Source: Demonstratio Mathematica
Authors: Julian Klukowski, Cecylia Łapińska
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $1,187
OpenAlex ID: W2782583834