The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

Let M be a compact, orientable, irreducible, ∂-irreducible, anannular 3manifold with one component T of ∂M a torus. A slope r on T is a T isotopy class of essential, unoriented, simple closed curves on T , and the distance between two slopes r1 and r2, denoted by 4(r1, r2), is the minimal geometric intersection number among all the curves representing the slopes. For a slope r on T , we denote ...

If K is a eld, let the ring R 0 consist of nite sums of homogeneous elements in R = Kx 1 ; x 2 ; x 3 ; : : : ]]. Then, R 0 contains M, the free semi-group on the countable set of variables fx 1 ; x 2 ; x 3 ; : : :g. In this paper, we generalize the notion of admissible order from nitely generated sub-monoids of M to M itself; assume that > is such an admissible order on M. We show that we can d...

A 3-manifold is ∂-reducible if ∂M is compressible in M . By definition, this means that there is a disk D properly embedded in M so that ∂D is an essential curve in ∂M . The disk D is called a compressing disk of ∂M , or a ∂-reducing disk of M . Now suppose M is a ∂-reducible manifold. Let K be a knot in a 3-manifold M such that ∂M is incompressible in M − K. A Dehn surgery on K is called ∂-red...

The Borel cardinality of the quotient of the power set of the natural numbers by the ideal Z0 of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space c0. We also show that a large collection of ideals introduced by Louveau and Veličkovič, with pairwise incomparable Borel cardinality, are all Borel reducible to c0. Thi...

Abstract A so-called semi-ideal model has been derived for a pulse-operated MEMS thermal flow sensor by reciprocal numerical mapping of the ideal an instantaneous line heat source to experimental data sensor. The novel not only applies as precise potential working equation but also provides insight into complete signal transmission chain from heater thermometers It gives answers prominent pecul...

Cuntz-Krieger algebras with exactly one non-trivial closed ideal are classiied up to stable isomorphism by the Cuntz invariant. The proof relies on RRrdam's classiication of simple Cuntz-Krieger algebras up to stable isomorphism and the author's classiication of two-component reducible topological Markov chains up to ow equivalence.

We consider the Hilbert scheme Hilb(Cd) of (d + 1) points in affine d-space C (d ≥ 3), which includes the square of any maximal ideal. We describe equations for the most symmetric affine open subscheme of Hilb(Cd), in terms of Schur modules. In addition we prove that Hilb(Cd) is reducible for n > d ≥ 12.

Self-assembled monolayers (SAMs) of a mu 3-eta 2:eta 2:eta 2-C60 triosmium cluster complex Os3(CO)8(CN(CH2)3Si(OEt)3)(mu 3-eta 2:eta 2:eta 2-C60) (2) on ITO or Au surface exhibit ideal, well-defined electrochemical responses and remarkable electrochemical stability being reducible up to tetranionic species in their cyclic voltammograms.