摘要:

A method is introduced or demonstrating that a category has no minimal generating class. This technique is then utilized to show that various categories have no minimal generating classes. These categories include the completely Hausdorff spaces and the regular completely Hausdorff spaces. They also include the categories of spaces which can be embedded in m-bounded Hausdorff spaces, in m-bounded T3spaces, in m-bounded completely Hausdorff spaces, in regular m-bounded completely Hausdorff spaces and products of KC spaces.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631939

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

In this note, we define the antisimple radical, A(M), of a Γ-ring M. A(M) is shown to be a special radical, and two characterizations of antisimple rings due to Szész are extended to Γ-rings. If R is the right operator ring of M, then A(R)* = A(M), where A(R) is the antisimple radical of R. If m,n are positive integers, then A(Mmn) = (A(M))mn, where Mmndenotes the group m x n matrices over M, considered as a Γnm-ring with the operations of matrix addition and multiplication.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631940

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Boundary value problems and variational inequalities, associated with second order elliptic operators, will be studied in a Hilbert space framework. In this space, functions will have (at least) locally square integrable derivatives of order up to two. Also the conormal derivative, extended by continuity, will be square integrable on the boundary of the region considered. Criteria for approximating elements of the Hilbert space by smooth functions will be given and thus closed convex sets, associated with inequalities on the boundary, exist.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631941

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A walk P in G is said to be a route if the length of P is at least one and no edge of G appears as two consecutive edge-terms of P. For n ≥ 2, a graph G is said to be (I*,n)-regular of degree k if each vertex of G is an end vertex of exactly k routes of length at most n-1. A complete characterization of (I*.n)-regular graphs is obtained.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631942

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A criterion, which ensures that the uniform dimension of a module equals that of its endomorphism ring, is presented and applied to cyclic modules. Furthermore, properties for a left ideal, for which the endomorphism ring of the associated cyclic module is a semi prime Goldie ring, are derived.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631943

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Transcendental and algebraic elements over commutative rings are defined. Rings with zero nil radical are considered. For a transcendental over R, necessary and sufficient conditions are derived for elements of R[α] to be algebraic or transcendental over R. For R a ring with identity and a finite number of minimal prime ideals, necessary and sufficient conditions are given for any element in a unitary overring of R to be algebraic or transcendental over R. It is proved that if α is algebraic Over R, so is every element of R[α]. It is show that if R is Noetherian, β is algebraic over R[α] and α is algebraic over R, then, under certain conditions, β is algebraic over R. If R has a finite number of minimal prime ideals, P1,…,Pk, which are pairwise comaximal, then if t is transcendental over R, R[t] can be obtained by adjoining k algebraic elements aiover R to R whose defining polynomials are in Pi[x], and conversely, if such elements are adjoined to R, they generate an element transcendental over R.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631944

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The problem of finding a formula for the clique number of the Paley graph G*(p) where p is a prime number such that p ≡ 1(mod 4) seems to be a hard one. These clique numbers are known for the caws 5 ⋚ p ⋚ 1601. In this paper we show that the clique number and chromatic number of the Paley graph G*(p2r) are both pr, where p is an odd prime and r is a natural number. Upper and lower bounds for the clique numbers and chromatic numbers of some related graphs are also determined.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631945

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The equations for the Lie point symmetries of autonomous systems of second order linear ordinary differential equations are derived. The results for a two dimensional system are treated in detail and some consideration is extended to higher dimensional systems. The effect of the introduction of time-dependent elements into the coefficient matrix is briefly discussed.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631946

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631947

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9631938

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor