Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local ...

We give new proofs of two theorems on rings in which every zero subring is finite; and we apply these theorems to obtain a necessary and sufficient condition for an infinite ring with periodic additive group to have an infinite periodic subring. 2000 Mathematics Subject Classification. 16N40, 16N60, 16P99. Let R be a ring and N its set of nilpotent elements; and call R reduced if N = {0}. Follo...

In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...

In a commutative f-ring, an 1-ideal I is called pseudoprime if ab = 0 implies a E I or b E I, and is called square dominated if for every a E I, lal < x2 for some x E A such that x2 E I. Several characterizations of pseudoprime 1-ideals are given in the class of commutative semiprime frings in which minimal prime 1-ideals are square dominated. It is shown that the hypothesis imposed on the f-ri...

In this paper ,we introduce a new type of rings,namely cosemiprime ringas generalization semiprime ring,where ring C is said to be if I= for each ideal I .Some properties rings are obtained . Also,we determin the relationship among types ideals in ring.

Let K/Q be a number field with euclidean ring of integers O. Let Γ be a finite-index torsion-free subgroup of the symplectic group Sp2n(O), and let N be the cohomological dimension of Γ. We exhibit a finite, geometrically-defined spanning set of H (Γ;Z) by generalizing the modular symbol algorithm of Ash and Rudolph for SLn(O).

 Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

The hydrazinium residue in the cation of the title salt, C(6)H(10)N(3)O(2)S(+)·Cl(-), is twisted out of the plane of the benzene ring to which it is attached [N-N-C-C torsion angle = 25.9 (2)°] and the amino group is almost perpendicular to the benzene ring [N-S-C-C torsion angle = 88.71 (16)°]. In the crystal, the cations are linked by N-H⋯O hydrogen bonds and π-π inter-actions [ring centroid ...

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...