摘要:

A notion of strongly prime is introduced for Γ-rings, and the class of strongly prime Γ-rings is shown to be special. Let M be a Γ-ring with left and right operator rings L and R, respectively. It is shown that s(L)+= so(M), and if M has both unities, then s(R)* = so(M). where s() and so() denote the strongly prime radical of a ring and a Γ-ring respectively. If m and n are positive integers, then so(Mmn) = so(M)mn, where Mmndenotes the set of ▪ x n matrices over M. considered as a Γamn-ring. The relationship of so(M) with the other radicals of M is discussed.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632150

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We show that a semisimple class of rings M satisfies condition (β) (i.e. I ◃ A ◃ M and A2= 0 implies A/I ε M) if and only if the corresponding radical class is hypersolvable or hypo-idempotent. Any radical class R which satisfies condition (F) (i.e. J ◃ I ◃ A and I/J ε R implies J ◃ A) must by hypo-idempotent. If the radical class is regular, the converse is also true. We also give characterizations of the semisimple classes of hypo-idempotent and subidempotent radical classes.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632151

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The circulant graph Cp> a1,…, ak< with 0 > a1>…> ak>(pt1)/2 has p vertices labeled 0,1,…,p-1 and x and y are adjacent if and only if x—y = ± ai(mod p) for some i. We prove the following regarding the chromatic index of a circulant: if d = gcd (a1,…, ak, p), then x' (Cp> al,…,ak) = Δ(C p > a1,…,ak) if and only if p/d is even.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632152

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A set B of vertices of a graph G = (V,E) is ak-maximal independent set(kMIS) if B is independent but for all ℓ-subsets X of B, where ℓ ⩽ k—1, and all (ℓ + 1)-subsets Y of V—B, the set (B—X) u Y is dependent. A set S of vertices of C is ak-maximal clique(kMc) of G iff S is a kMIS of Ǥ. Let βk, (G) (wk(G) respectively) denote the smallest cardinality of a kMIS (kMC) of G—obviously βk(G) = wk(Ǥ). For the sequence m1⋚ m2⋚…⋚ mn= r of positive integers, necessary and sufficient conditions are found for a graph G to exist such that wk(G) = mkfor k = 1,2,…,n and w(G) = r (equivalently, βk(G) = mkfor k = 1,2,…,n and β(G) = r). Define sk(ℓ,m) to be the largest integer such that for every graph G with at most sk(ℓ,m) vertices, βk(G) ⩽ ℓ or wk(G) ⩽ m. Exact values for sk(ℓ,m) if k ≥ 2 and upper and lower bounds for s1(ℓ,m) are de termined.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632153

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Let A be a unitary Banach algebra and let B be a closed subalgebra of A that contains the unit. For an element of B we show in this note how both the singular and exponential spectrum depends on the algebra.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632154

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The pseudo-projective plane M(q) is obtained by attaching a two cell to a circle by a map of degree q. We here determine the homotopy classes (M(q), M(w)) and some of their properties in the unbased, based and cellular-preserving cases. In the cellular-preserving case the sets have a near-ring structure for q = w but the addition is lost on passing to the based case. The results, known for q = w = 2, are compared to the known result for ϵ(M(q)) the group of based self-homotopy equivalence classes.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632155

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A survey is given of various generalizations of the Whitehead product. Carrying the procedure a step further, a generalization is given that specialized in one wry relates to the “Whitehead elements” in the (mod p) kernel of the double suspension (p an odd prime, p > 4). Specialized in another way the product relates to the action of the Q-homomorphism (in the EHQ sequence) on elements that are not double suspensions.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632156

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

For the algebraic sphere S2defined as the zero set of the equation x21+ x22+ x23= 1 in C3, we see that there are polynomial maps fn: S2→ S2of each degree. For the algebraic sphere S2defined as the suspension of S1= C-(0) in the categoryAFFCof based affine schemes of countable type over C, the set HomAFFC(S2, S2) modulo homotopy is seen, using standard definitions adapted to our algebraic situation, to be (ZxZ)/ψ where ψ collapses (Zx0) ∪ (0xZ) to a point.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632157

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632158

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632159

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor