Let α denote an infinite cardinal or ∞ which is used to signify no cardinal constraint. This work introduces the concept of an αcc-Baer ring and demonstrates that a commutative semiprime ring A with identity ...

A Conrad frame is a frame which is isomorphic to the frame C(G) of all convex ℓ-subgroups of some lattice-ordered group G. It has long been known that Conrad frames have the disjointification property. In ...

Hewitt [Rings of real-valued continuous functions. I., Trans. Amer. Math. Soc. 64 (1948), 45–99] defined the m-topology on C(X), denoted Cm(X), and demonstrated that certain topological properties of X could be characterized by certain topological ...

The functor on the category of bounded lattices induced by reversing their order, gives rise to a natural equivalence of coherent frames. We investigate the spectra as well as some well-known frame properties like zero-dimensionality ...

The well-known Jaffard–Ohm–Kaplansky Theorem states that every abelian ℓ-group can be realized as the group of divisibility of a commutative Bézout domain. To date there is no realization (except in certain circumstances) of an arbitrary, ...

We determine those unoriented cobordism classes which can be realized by a manifold whose tangent bundle splits into a sum of real (complex) line bundles.