摘要:

In this paper we introduce the concept of a semi-terminal object in a category. Analogous to the fact that limit sources are terminal objects in comma categories we have that mono-sources are semi-terminal objects in comma categories.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631895

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this brief note, we are concerned with two problems. First we study the units of RG when R is commutative and G is right-ordered. Earlier results of the author and also of Karpilovsky are improved. Secondly, we show that if R and S are P. I. D.'s which do not contain fields and R>x< = S>x<, then R = S.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631896

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this paper we define two concepts of prime ideals for Ω-groups. The first generalizes the definitions of prime ideal in rings, nearrings, Γ-rings, associative algebras and Lie algebras. The second generalizes a concept defined for groups by Ščukin ([21]). We show that both lead to radicals in the sense of Hoehnke ([10]). Furthermore in the case of rings, Γ-rings, abelian zero-symmetric nearrings and cubic rings these two definitions coincide, thus obtaining a new characterization for the prime ideal. Zero-symmetric Ω-groups are defined analogously to the nearring case and a new characterization in term of ideals is given.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631897

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The author has recently developed a gradient-only dynamic method for unconstrained minimization. The main drawback of this method is, that in spite of rapid motion towards the neighbourhood of a local minimum, the final convergence is slow. To improve the situation the possibility of switching from the dynamic method to a conjugate qradient type method near the minimum is investigated. The Fletcher-Reeves conjugate gradient method is applied in a way in which only gradient evaluations are used by exploiting an Euler—trapezium integration scheme. The numerical results obtained are promising, indicating the combined method to be competitive for problems of high dimensionality and where the gradient evaluations are re1atively inexpensive.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631898

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In [2] van der Walt called a left ideal L of a ring A,left strongly nil, if given 1 ε L and k ε K, K a left ideal. there is an n such that (1+k)nε K. L is called left stronglynilpotentif for any left ideal K there exists an m such that (L+K)m⊆ K. In this paper we will prove that if A is a left artinian ring (not necessarily with unity) then every left strongly nil left ideal is left strongly nilpotent. This result is a generalization of the main theorem of [2].

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631899

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this paper it is proved that if T:A→Xis a topological functor satisfying certain conditions, then there is a Galois Connection between the class of bireflective subcategories ofAand the class of epireflective subcategories ofAthat are not bireflective and that are contained in the subcategory of separated objects ofA. In general such a correspondence is not bijective.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631900

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

An adaptation of a theorem by Herrlich [5] shows that every initially structured category A can be fully embedded in a topological category AC, which is, in fact, a MacNeille completion of A. It is then shown that A is Cartesian closed if and only if ACis.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631901

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Let R be an associative ring with 1. It is well known (see [1], [2]) that if R is commutative, then R is Yon Neumann regular (VNR) <=> the polynomial ring S = R[x] is semihereditary. While one of these implications is true in the general case, it is known that a polynomial ring over a regular ring need not be semihereditary (see [3]). In [4] we showed that a ring R is VNR <=> aS + xS is projective for each a ε R. In this note we sharpen this result and use it to show that if c is the ring epimorphism from R[x] to R that maps each polynomial onto its constant term, then R is Yon Neumann regular <=> the inverse image (under c) of each principal (right, left) ideal of R. is a principal (right. left) ideal of R[x] generated by a regular element. (Here an element is regular if and only if it is a non zero-divisor).

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631902

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

We prove that if x = y+μ[δ(ü):-1Δ(μ)y is the unique solution of the equation x-üTx = y in a Banach space, with δ(ü) the Fredholm divisor of the operator T, and Δ an entire function of the complex variable ü, then Δ satisfies an exponential growth estimate of the form exp(clü|P). The proof holds for all operators T belonging to a certain quasi-normed operator ideal A with the property that A(p)supports a continuous trace. This result was known to hold for operators belonging to the approximative kernel of A, and it was conjectured by H König to be true generally. As a corollary we state general conditions implying the density of the set of eigenvectors of an operator.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631903

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631904

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor