The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
In this paper, we establish the following results: (i) every strongly finite dilator is finitely presentable in the category of endofunctors on the category of ordinals; (ii) a dilator F is strongly finite if and only if F is finitely presentable in the category of dilators.
Given a locale and a join semilattice with bottom element , a new concept called -slice is defined,where is as an action of the locale on the join semilattice . The -slice adopts topological properties of the locale through the action . It is shown that for each , is an interior operator on .The collection is a Priestly space and a subslice of -. If the locale is spatial we establish an isomorphism between the -slices and . We have shown that the fixed set of ,...
The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.
This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.
Does there exist an atomic Archimedean lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question is given.