In the title mol-ecule, C(37)H(38)O(6), the non-fused C atom belonging to the five-membered ring of the fluorene system is connected to two p-phenyl-ene rings, the rings opening up the C(ar-yl)-C-C(ar-yl) angle to 113.1 (1)°. The four-atom -O-CH(2)-C(=O)-O- chain between the p-phenyl-ene ring and the tert-butyl group assumes a more regular W-shaped conformation for one substituent [O-C-C-C tors...

For a regular ring R and an affine monoid M the homotheties of M act nilpotently on the Milnor unstable groups of R[M ]. This strengthens the K2 part of the main result of [G5] in two ways: the coefficient field of characteristic 0 is extended to any regular ring and the stableK2-group is substituted by the unstable ones. The proof is based on a polyhedral/combinatorial techniques, computations...

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

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 [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

Given an iterated skew polynomial ring C[y1; τ1, δ1] . . . [yn; τn, δn] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m+ 〈y1, y2, . . . , yn〉 is an iterated skew power series ring. When C is a field, this completion is a local, noetherian, Auslander regular domain with Krull, classical Krull and global dimension all equ...

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...

Let (R,m) denote an n-dimensional Gorenstein ring. For an ideal I ⊂ R of height c we are interested in the endomorphism ring B = HomR(H c I (R),H c I (R)). It turns out that B is a commutative ring. In the case of (R, m) a regular local ring containing a field B is a Cohen-Macaulay ring. Its properties are related to the highest Lyubeznik number l = dimk Ext d R(k, H c I (R)). In particular R ≃...