Let X be a completely regular topological space. An intermediate ring is a ring A(X) of continuous functions satisfying C∗(X) ⊆ A(X) ⊆ C(X). In Redlin andWatson (1987) and in Panman et al. (2012), correspondencesZ A andZ A are defined between ideals in A(X) and z-filters onX, and it is shown that these extend the well-known correspondences studied separately for C∗(X) andC(X), respectively, to ...

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.

in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

Let X be a completely regular topological space. An intermediate ring is a ring A(X) of continuous functions satisfying C∗(X) ⊆ A(X) ⊆ C(X). We give a characterization of C(X) in terms of extensions of functions in A(X) to real-compactifications of X. We also give equivalences of properties involving the closure in the real-compactifications of X of zero-sets in X; we use these equivalences to ...

7,8-Dihydrobatrachotoxinin A is an intermediate in the synthesis of batrachotoxin, the extremely potent venom from the Colombian frog Phyllobates aurotaenia. A crystal structure analysis by x-ray diffraction has confirmed that the intermediate is identical with the natural batrachotoxinin A except for the saturation of the C(7)-C(8) bond. There are seven asymmetric carbon atoms in the molecule....

A 14-step total synthesis of (+/-)-salinosporamide A (1), a potent inhibitor of the 20S proteasome isolated from the marine bacterium Salinospora tropica, is described. The synthesis is based on a diastereoselective intramolecular aldolisation of a substituted beta-keto amide intermediate, i.e. 13, derived from a beta-keto acid, viz. 21, and an alpha-amino malonate, leading to the pyrrolidinone...