Add to ORKGWe provide a method to construct a type of orthomodular structure known as an orthoalgebra from the direct product decompositions of an object in a category that has finite products and whose ternary product diagrams give rise to certain pushouts. This generalizes a method to construct an orthomodular poset from the direct product decompositions of familiar mathematical structures such as non-empty sets, groups, and topological spaces, as well as a method to construct an orthomodular poset from the complementary pairs of elements of a bounded modular lattice. KEY WORDS: orthomodular poset; orthoalgebra; decomposition; product; category. Mathematics Subject Classifications (2000): 06C15, 81P10, 03G12, 18A3
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp ortho...
In this paper, we consider a generalization of the notion of orthomodularity for posets to the conce...
Abstract. We present a method of constructing an orthomodular poset from a relation algebra. This te...
Abstract. Let L be an orthomodular lattice. For a, b ∈ L define a↔cb if either a and b both belong t...
1862), it was shown that the direct product decompositions of a set X naturally form an orthomodular...
summary:It is proved that orthomodular posets are in a natural one-to-one correspondence with certai...
Summary. The main result of the article is the solution to the problem of short axiomatizations of o...
summary:It is proved that orthomodular posets are in a natural one-to-one correspondence with certai...
In 1996, Harding showed that the binary decompositions of any algebraic, relational, or topological ...
AbstractBeginning with the external point of view we show how orthomodular lattices may be “pasted” ...
Abstract. If X is a variety of orthomodular lattices generated by a finite orthomodular lattice the ...
summary:We prove that an orthomodular lattice can be considered as a groupoid with a distinguished e...
Abstract. If/C is a variety of orthomodular l ttices generated by a set of orthomodular l ttices hav...
The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp ortho...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp ortho...
In this paper, we consider a generalization of the notion of orthomodularity for posets to the conce...
Abstract. We present a method of constructing an orthomodular poset from a relation algebra. This te...
Abstract. Let L be an orthomodular lattice. For a, b ∈ L define a↔cb if either a and b both belong t...
1862), it was shown that the direct product decompositions of a set X naturally form an orthomodular...
summary:It is proved that orthomodular posets are in a natural one-to-one correspondence with certai...
Summary. The main result of the article is the solution to the problem of short axiomatizations of o...
summary:It is proved that orthomodular posets are in a natural one-to-one correspondence with certai...
In 1996, Harding showed that the binary decompositions of any algebraic, relational, or topological ...
AbstractBeginning with the external point of view we show how orthomodular lattices may be “pasted” ...
Abstract. If X is a variety of orthomodular lattices generated by a finite orthomodular lattice the ...
summary:We prove that an orthomodular lattice can be considered as a groupoid with a distinguished e...
Abstract. If/C is a variety of orthomodular l ttices generated by a set of orthomodular l ttices hav...
The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp ortho...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp ortho...
In this paper, we consider a generalization of the notion of orthomodularity for posets to the conce...