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...

We define type A, type B, type C as well as C∗-semi-finite C∗-algebras. It is shown that a von Neumann algebra is a type A, type B, type C or C∗-semi-finite C∗-algebra if and only if it is, respectively, a type I, type II, type III or semi-finite von Neumann algebra. Moreover, any type I C∗-algebra is of type A (actually, type A coincides with the discreteness as defined by Peligrad and Zsidó),...

The Hilbert scheme H n of n points in A contains an irreducible component R n which generically represents n distinct points in A. We show that when n is at most 8, the Hilbert scheme H n is reducible if and only if n = 8 and d ≥ 4. In the simplest case of reducibility, the component R 8 ⊂ H 8 is defined by a single explicit equation which serves as a criterion for deciding whether a given idea...

We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...

We will drop the compactness hypothesis on G in the results of §6, doing this in such a way that problems can be reduced to the compact case. This involves the notions of reductive Lie groups and algebras and Cartan involutions. Let © be a Lie algebra. A subalgebra S c © is called a reductive subaU gebra if the representation ad%\® of ίΐ on © is fully reducible. © is called reductive if it is a...

Tetra-n-butylammonium bromide forms the title semi-clathrate hydrate crystal, C16H36N+.Br-.38H2O, under atmospheric pressure. The cation and anion lie at sites with mm symmetry and seven water molecules lie at sites with m symmetry in space group Pmma. Br- anions construct a cage structure with the water molecules. Tetra-n-butylammonium cations are disordered and are located at the centre of fo...

Let us assume there exists a super-abelian, Erdős–Fibonacci, closed and isometric composite isomorphism. Is it possible to study integrable, semi-Noether, maximal matrices? We show that there exists a multiply onto, almost everywhere smooth, algebraic and reducible Riemannian functor. It has long been known that every pairwise super-prime homomorphism equipped with a super-universally contra-Ei...

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...