we observe some new characterizations of $n$-presented modules. using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

The title compound, C25H24N3O3P, was obtained by catalytic phospho-nation of 4'-(4-bromphen-yl)-2,2':6',2''-terpyridine. The terpyridine moiety is nearly planar, the dihedral angles between the central and the outer rings being 4.06 (9) and 5.39 (9)°. The N atoms in the two pyridine rings are oriented nearly anti-periplanar to that of the central ring. The benzene ring is rotated out of the pla...

Given a finite metacyclic group G, a central extension F having the projective lifting property over all fields is constructed. This extension and its group rings are used to investigate the faithful irreducible projective representations of G and the fields over which they can be realized. A full description of the finite metacyclic groups having central simple twisted group rings over fields ...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

The mol-ecular structure of the title compound, C(17)H(20)N(4)O(5), contains a central fused-ring system, comprised of six- and five-membered rings. This unit is linked by C(2) chains to two 2-oxo-1,3-oxazolidine five-membered rings. The central fused-ring system is essentially planar, with a maximum deviation of 0.008 (1) Å from the mean plane. Both oxazolidine five-membered rings are also nea...

In the title compound, C(31)H(25)ClO(3), the central ring of the xanthene core shows a shallow boat conformation, while the outer six-membered rings display envelope conformations. The dihedral angle between the outer aromatic rings is 88.1 (3)° and the dihedral angles between the chloro-benzene ring and the two phenyl rings are 69.5 (2) and 69.6 (2)°.