It is proved that if $\varphi\colon A\to B$ a local homomorphism of commutative noetherian rings, nonzero finitely generated $B$-module $N$ whose flat dimension over $A$ at most $\mathrm{edim}\, A - \mathrm{edim}\, B$, free $B$, and $\varphi$ special type complete intersection. This result motivated by "patching method" developed Taylor Wiles, conjecture de Smit, the first author, dealing with ...

Let (R, m) and (S, n) be commutative Noetherian local rings, and let φ : R→ S be a flat local homomorphism such that mS = n and the induced map on residue fields R/m→ S/n is an isomorphism. Given a finitely generated R-module M , we show that M has an S-module structure compatible with the given R-module structure if and only if Ext R (S,M) = 0 for each i ≥ 1. We say that an S-module N is exten...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

In this paper, all rings are associative with identity and all modules are unital left modules unless otherwise specified. Let R be a ring and M a module. N ≤M will mean N is a submodule of M. A submodule E of M is called essential in M (notation E ≤e M) if E∩A = 0 for any nonzero submodule A of M. Dually, a submodule S of M is called small in M (notation S M) if M = S+T for any proper submodul...

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

This paper describes a method of Automatic Arabic Character Recognition (ACR). This system is articulated around four distinct modules which are the main image processing given by: a module of treatment, a module of segmentation, a module of recognition and a module of detection of symbols of classification. For classification; we have used Fuzzy Logic (FL), Genetic Algorithm (GA), and Expert S...

The purpose of this paper is to present a novel contour code feature in conjunction with a rule based segmentation for cursive handwriting recognition. A heuristic segmentation algorithm is initially used to over segment each word. Then the prospective segmentation points are passed through the rule-based module to discard the incorrect segmentation points and include any missing segmentation p...

A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p > 3. Let ρ be a continuous homomorphism from the absolute Galois group of Q to GL(3,F) which is isomorphic to a direct sum of a character and a two-dimensional odd irreducible representation. We assume that the image of ρ is contained in the intersection of the stabilizers of the line spanned by ...

We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p > 3. Let ρ be a continuous homomorphism from the absolute Galois group of Q to GL(3,F) which is isomorphic to a direct sum of a character and a two-dimensional odd irreducible representation. We assume that the image of ρ is contained in the intersection of the stabilizers of the line spanned by ...