Daily-life foldable items, such as popup tents, the curved origami sculptures exhibited in the Museum of Modern Art of New York, overstrained bicycle wheels, released bilayered microrings and strained cyclic macromolecules, are made of rings buckled or folded in tridimensional saddle shapes. Surprisingly, despite their popularity and their technological and artistic importance, the design of su...

In this paper, a combination of algebraic and topological methods are applied to obtain new structural results on harmonic rings. Especially, it is shown that if Gelfand ring A modulo its Jacobson radical zero dimensional ring, then clean ring. It also proved that, for given A, the retraction map $${\text {Spec}}(A)\rightarrow {\text {Max}}(A)$$ flat continuous only Dually, mp-ring {Min}}(A)$$...

This series of lectures is about algebraic aspects of real algebraic geometry. Partially ordered rings (porings) occur very naturally in real algebraic geometry, as well as in other branches of mathematics. There is a rich classical theory of porings (the beginnings dating back to the 1930s and 1940s). To a large extent it was inspired by the study of rings of continuous functions in analysis a...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

This paper is a continuation of work done by the present author together with P. R. Hall [1]. We characterise the prime and equiprime radicals of N0(G) for certain topological groups G. Various results are obtained concerning primeness and strongly primeness for the sandwich near-ring N0(G,X, θ). MSC 2000: 16Y30, 22A05