For a semigroup S (group G) we study relational equations and describe all semigroups with equationally Noetherian direct powers. It follows that any group G has powers if consider as an algebraic structure of certain language. Further specify the results follows: power finite is Noetherian, then minimal ideal Ker(S) rectangular band groups coincides set reducible elements

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

Computational methods for finding the character table of a finite group require a stock of reducible characters and techniques for decomposing these characters into irreducible characters. A method for generating reducible characters from a representation of a group is proposed. Several new techniques for computing the irreducible decompositions of a set of characters are given; these technique...

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.

In this paper we determine all non-trivial self-motions of TSSM manipulators with two parallel rotary axes which equals the determination of all flexible octahedra where one vertex is an ideal point. This study also closes the classification of these motions for the whole set of parallel manipulators of TSSM type. Our approach is based on Kokotsakis meshes and the reducible compositions of sphe...

A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...

Derivang the min imum and maximum global snapshots is very useful f o r some error detection problems in distributed programs. Several researchers, e.g., Groselj, Chen and W u , have shown that the min imum and maximum global snapshot problems are lineart ime reducible to the max imum constant-ratio network flow (MCNF) problem, here defined as the well-known maximum network flow problem with m ...

We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ERs of a family which includes Polish actions of S∞, the group of all permutations of N, and is closed under the Fubini product modulo the ideal Fin of all finite sets, and some other operations. Our second main result shows that T2, an equivalence relation called “the...