Let $R$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎A right $R$-module $M$ is called $(n‎, ‎d)$-projective if $Ext^{d+1}_R(M‎, ‎A)=0$ for every $n$-copresented right $R$-module $A$‎. ‎$R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $R$-module is $(n‎, ‎d)$-projective‎. ‎$R$...

let d be a division ring with centre k and dim, d< ? a valuation on k and v a noninvariant extension of ? to d. we define the initial ramfication index of v over ?, ?(v/ ?) .let a be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to d with valuation rings a , a ,…, a . if b= a , it is shown that the following conditions are equivalent: (i) b is a finite...

Let D be a division ring with centre K and dim, D< ? a valuation on K and v a noninvariant extension of ? to D. We define the initial ramfication index of v over ?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation rings A , A ,…, A . If B= A , it is shown that the following conditions are equivalent: (i) B i...

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...

In this work, we investigate the transfer of some homological properties from a ring $R$ to its amalgamated duplication along some ideal $I$ of $R$ $Rbowtie I$, and then generate new and original families of rings with these properties.

The Cassini spacecraft has provided the first clear images of the D ring since the Voyager missions. These observations show that the structure of the D ring has undergone significant changes over the last 25 years. The brightest of the three ringlets seen in the Voyager images (named D72), has transformed from a narrow, <40-km wide ringlet to a much broader and more diffuse 250-km wide feature...

In this research at the first complex and its halogenated derivatives were optimized. NBO calculations and NMR for the complexes were carried out at the B3LYP/6-31G*quantum chemistry level. In the 1- (4-fluorophenyl) -2, 3-dihydro-1 H-naphto- [1, 2-e] [1, 3] oxazine-3-n, there are 4 rings, respectively, rings from the side attached to the halogen They are named C, B, A, and D. Calculations and ...

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.