In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as subalgebra the ring invariants certain noncommutative with respect to action $S_1\times S_2\times\cdots\times S_n$, where $S_j$ is symmetric group on $j$ variables. An interesting question what similar algebra would be in invariant product alternating groups. this paper we define such an algebra, denoted $\mathscr...

We introduce a notion of amenable normal extension S unital ring R with finite approximation system F, encompassing the algebras over field Gromov and Elek, twisted crossed product by an group, tensor extension. It is shown that every Sylvester matrix rank function rk preserved has canonical to rk_F for S. In case extension, it also depends on continuously. When group action C*-algebra preservi...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called emph{affine subgroups.}~the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_...

Two characterizations of an Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special Galois system is determined by the trace of the Galois group.

the purpose of this study was to investigate the effects of short term creatine monohydrate as an ergogenic supplement on the sprint performance and muscular strength of wrestlers. 20 wrestlers were selected randomly and divided into two groups. one group was placebo group (control) and the other group was creatine supplement group (experimental). in a double blind project, subjects' speed...