A set A is m-reducible (or Karp-reducible) to B if and only if there is a polynomial-time computable function f such that, for all x, x ∈ A if and only if f(x) ∈ B. Two sets are: • 1-equivalent if and only if each is m-reducible to the other by one-one reductions; • p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and • p...

Let (M ;⊆) and (L ;⊆) be the lattices of additive induced-hereditary properties of graphs and additive hereditary properties of graphs, respectively. A property R∈Ma (∈ L) is called a minimal reducible bound for a property P∈Ma (∈ L) if in the interval (P;R) of the lattice M (L) there are only irreducible properties. The set of all minimal reducible bounds of a property P∈Ma in the lattice M we...

In this paper, we define the notion of minimal prime ideals hoops and investigate some properties them. Then by using annihilators, study relation between annihilators. Also, introduce zero divisors elements prove that set all is a union hoop. Finally, notions maximal hoop, two new as p-ideal m-ideal. them every semi-simple hoop an m-ideal it.

We study properties of a C2-cofinite vertex operator algebra V = ⊕ ∞ i=0Vi of CFT type. If it is also rational (i.e. all modules are completely reducible) and V ′ ∼= V , then the rigidity of the tensor category of modules has been proved by Huang [11], where V ′ denotes the restricted dual of V . However, when we treat irrational C2cofinite VOAs, the rigidity is too strong, because it is almost...

A sufficient condition for a monic integer polynomial to be a semi-CNS polynomial is presented. This result infers a unified proof of two well-known theorems on irreducible CNS polynomials thereby extending them to reducible polynomials.

We investigate Tukey functions from the ideal of all closed nowhere dense subsets of 2N. In particular, we answer an old question of Isbell and Fremlin by showing that this ideal is not Tukey reducible to the ideal of density zero subsets of N. We also prove non-existence of various special types of Tukey reductions from the nowhere dense ideal to analytic P-ideals. In connection with these res...

We show that the distance between a finite filling slope and a reducible filling slope on the boundary of a hyperbolic knot manifold is at most one. Let M be a knot manifold, i.e. a connected, compact, orientable 3-manifold whose boundary is a torus. A knot manifold is said to be hyperbolic if its interior admits a complete hyperbolic metric of finite volume. Let M(α) denote the manifold obtain...

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.