We prove a version of B ezout's theorem for non-commutative analogues of the projective spaces P n. 0. Introduction Throughout we work over an algebraically closed eld k. We establish a version of B ezout's Theorem for non-commutative projective spaces, quantum P n s for short. If Y is a quantum P n then the alternating sum of the dimension of the Ext-groups gives a bilinear form : K 0 (Y) K 0 ...

Let Moldn,d be the moduli of rank d subalgebras Mn over Z. For x∈Moldn,d, let A(x)⊆Mn(k(x)) subalgebra corresponding to x, where k(x) is residue field x. In this article, we apply Hochschild cohomology Moldn,d. The dimension tangent space TMoldn,d/Z,x Z at x can calculated by H1(A(x),Mn(k(x))/A(x)). We show that H2(A(x),Mn(k(x))/A(x))=0 a sufficient condition for canonical morphism Moldn,d→Z be...

X iv :0 81 2. 43 67 v1 [ cs .D M ] 2 3 D ec 2 00 8 ON SOME CLASSES OF FUNCTIONS AND HYPERCUBES DIMITER STOICHKOV KOVACHEV Abstra t. In this paper, some lasses of dis rete fun tions of k-valued logi are onsidered, that depend on sets of their variables in a parti ular way. Obtained results allow to " onstru t" these fun tions and to present them in their tabular, analyti al or matrix form, that ...

Renal responses were quantified in northern elephant seal (Mirounga angustirostris) pups during their postweaning fast to examine their excretory capabilities. Pups were infused with either isotonic (0.9%; n = 8; Iso) or hypertonic (16.7%; n = 7; Hyper) saline via an indwelling catheter such that each pup received 3 mmol NaCl/kg. Diuresis after the infusions was similar in magnitude between the...

Classical differential geometry can be encoded in spectral data, such as Connes’ spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes’ non-commutative spin geometry encompassing noncommutative Riemannian, symplectic, complex-Hermitian and (Hyper-) Kähler geometry...

We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive implicative ordered filter. We also give equivalent conditions of positive implicative ordered f...

The first author proved in a previous paper that the n-fold bar construction for commutative algebras can be generalized to En-algebras, and that one can calculate Enhomology with trivial coefficients via this iterated bar construction. We extend this result to En-homology and En-cohomology of a commutative algebra A with coefficients in a symmetric A-bimodule.

Let K(n) be the n Morava K–theory at a prime p, and let T (n) be the telescope of a vn–self map of a finite complex of type n. In this paper we study the K(n)∗–homology of Ω ∞X, the 0 space of a spectrum X, and many related matters. We give a sampling of our results. Let PX be the free commutative S–algebra generated by X: it is weakly equivalent to the wedge of all the extended powers of X. We...

ion of shortest-paths problem: Definition 19. A commutative semi-ring is a set K and two operations ⊗,⊕ satisfying: 1. ⊕ is commutative and associative; there is an identity “0” s.t. k + 0 = k for all k ∈ K. 2. ⊗ is commutative and associative; there is a multiplicative identity “1” s.t. k ⊗ 1 = k for all k ∈ K. 3. The distributive law holds: a⊗ (b⊕ c) = (a⊗ b)⊕ (a⊗ c). Definition 20. The min-s...