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 the title compound, C(6)H(5)N(3)O·C(13)H(11)N(3)O, the benzo-triazole ring system in the 1-benzyl-1H-benzotriazole 3-oxide (A) mol-ecule is close to being planar (r.m.s. deviation = 0.011 Å); its mean plane forms a dihedral angle of 67.56 (7)° with that of the attached phenyl ring. The benzotriazole ring system in the 1-hy-droxy-benzotriazole (B) mol-ecule is also close to being planar (r.m....

In the title compound, C(13)H(10)N(4)O(5), the aromatic ring planes are close to perpendicular [dihedral angle = 75.94 (5)°] and the C-N-N-C torsion angle is 88.7 (2)°. Both nitro groups lie close to their attached ring plane, with C-C-N-O torsion angles of 3.1 (2) and 5.3 (2)°. This allows for the formation of an intra-molecular N-H⋯O hydrogen bond, which closes an S(6) ring. In the crystal, N...

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...

The central five-membered ring of the title compound, C(18)H(15)N(3)OS, is almost planar (r.m.s. deviation = 0.028 Å) and the benzothia-zole fused-ring system is close to coplanar with this ring [dihedral angle = 6.1 (1)°]. The phenyl substituent is twisted by 62.5 (1)°.

In the title compound, C(15)H(19)ClN(4)O(3), an active agrochemical possessing insecticidal activity, the dihedral angle between the mean planes passing through the pyridine ring and the five-membered ring is 87.3 (2)°. The fused pyridine ring adopts a twisted sofa conformation. The mol-ecular structure features close intra-molecular C-H⋯N and C-H⋯O hydrogen bonding.

In the title compound, C(13)H(22)N(4)O(2)S(2), the six-membered ring displays a half-chair conformation. The olefin amine unit is close to being coplanar with the imidazolidine ring (r.m.s. deviation = 0.059 Å). The dithiol-ane ring adopts a twisted conformation. In the crystal, mol-ecules are linked by weak C-H⋯O inter-actions.

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

The title compound, C(7)H(13)N(5), a tetrazole analogue of betaines, exists as a zwitterion, with the H atom of the tetrazole ring being transferred to the piperidine ring N atom. The tetrazole ring symmetry is close to C(2v), which suggests strong charge delocalization in the N-C-N fragment of the ring. There are classical hydrogen bonds in the structure which are responsible for the formation...