On semi-topological rings

On (Semi)Topological $BL$-algebras

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

On Splitting of Extensions of Rings and Topological Rings

Several results on splitting of extensions of Banach algebras are generalized to the case of (not necessarily commutative, not necessarily unital) rings or topological rings. Detailed proofs of the results are provided.

On Strictly Minimal Topological Division Rings

On λ-rings and topological realization

A λ-ring is, roughly speaking, a commutative ring R with unit together with operations λi, i ≥ 0, on it that act like the exterior power operations. It is widely used in algebraic topology, algebra, and representation theory. For example, the complex representation ring R(G) of a group G is a λ-ring, where λi is induced by the map that sends a representation to its ith exterior power. Another e...

Topological Heterotic Rings

We prove the existence of topological rings in (0,2) theories containing non-anomalous left-moving U(1) currents by which they may be twisted. While the twisted models are not topological, their ground operators form a ring under non-singular OPE which reduces to the (a,c) or (c,c) ring at (2,2) points and to a classical sheaf cohomology ring at large radius, defining a quantum sheaf cohomology...