The maximality property was introduced in [9] in orthomodular posets as a common generalization of orthomodular lattices and orthocomplete orthomodular posets. We show that various conditions used in the theory of e ...

It is an old open question whether a t-norm with a continuous diagonal must be continuous [7]. We give a partial positive answer for t-norms with noncontinuous additive generators (constructed by the technique of [1, ...

We introduce two new classes of orthomodular posets—the class of weakly Boolean orthomodular posets and the class of orthomodular posets with the property of maximality. The main result of this paper is that the ...

The notion of spectral automorphism of an orthomodular lattice was introduced by Ivanov and Caragheorgheopol [3] to create an analogue of the Hilbert space spectral theory in the abstract framework of orthomodular lattices. ...

Compression base effect algebras were recently introduced by Gudder [6]. They generalize sequential effect algebras [7] and compressible effect algebras [5]. The present paper focuses on atomic compression base effect ...

Various conditions ensuring that a sequential effect algebra or the set of sharp elements of a sequential effect algebra is a Boolean algebra are presented.

It is proved that two di erent common generalizations of orthocomplete and lattice e ect algebras coincide within the class of separable Archimedean e ect algebras.

Connections between the weak orthocompleteness and the maximality property in e ect algebras are presented. It is proved that an orthomodular poset with the maximality property is disjunctive. A characterization of ...

We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.

We show that a commutative bounded integral orthomodular lattice is residuated iff it is a Boolean algebra. This result is a consequence of [7, Theorem 7.31]; however, our proof is independent and uses other instruments.