Let M be an Artinian module over the commutative ring A (with nonzero identity) and a p spec A be such that a is a finitely generated ideal of A and aM = M. Also suppose that H = H where H. = M/ (0: a )for i

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

Let f be a modular eigenform of weight at least two and let F be a finite abelian extension of Q. Fix an odd prime p at which f is ordinary in the sense that the p Fourier coefficient of f is not divisible by p. In Iwasawa theory, one associates two objects to f over the cyclotomic Zp-extension F∞ of F : a Selmer group Sel(F∞, Af ) (whereAf denotes the divisible version of the two-dimensional G...

The system Galactica of free access is supplemented module for the Coulomb interaction. It is based on a high-precision method for solving differential equations of motion of N charged particles. The paper presents all the theoretical and practical issues required to use this module of system Galactica so that even the beginning researcher could study the motion of particles, atoms and molecules.

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...