for some real number X, the symbol V denoting the lattice least upper bound. Any ring R is regular [10] if for each xER there is an xaER such that xx°x = x. It is evident that every regular F-ring R contains a maximal bounded sub-F-ring R, the F-ring of all xER satisfying equation (1.1). The relationship between a regular F-ring and its maximal bounded sub-F-ring is analogous to that between th...

This paper introduces a new concept called controllable ring signature which is ring signature with additional properties as follow. (1) Anonymous identification: by an anonymous identification protocol, the real signer can anonymously prove his authorship of the ring signature to the verifier. And this proof is non-transferable. (2) Linkable signature: the real signer can generate an anonymous...

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

The real closed valuation rings, i.e., convex subrings of real closed fields, form a proper subclass of the class of real closed domains. It is shown how one can recognize whether a real closed domain is a valuation ring. This leads to a characterization of the totally ordered domains whose real closure is a valuation ring. Real closures of totally ordered factor rings of coordinate rings of re...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.