共查询到9条相似文献,搜索用时 0 毫秒
1.
Kevin C. O’Meara 《代数通讯》2017,45(5):2186-2194
A classical and clever construction by George Bergman in the mid 1970s was of a unit-regular algebra Q (over an arbitrary field F) that contains a regular subalgebra R which is not unit-regular. The algebra Q was constructed inside a full linear ring of an uncountable-dimensional vector space over F. Here we give a much simpler construction of Bergman’s R and Q inside an algebra B of countably-infinite matrices. The algebra B does not seem to have been noticed before, possibly because it is not obviously a ring. It also suggests possibilities for answering the difficult open problem of constructing a non-separative regular ring. 相似文献
2.
LetA
e
be the algebra obtained by adjoining identity to a non-unital Banach algebra (A, ∥ · ∥). Unlike the case for aC*-norm on a Banach *-algebra,A
e
admits exactly one uniform norm (not necessarily complete) if so doesA. This is used to show that the spectral extension property carries over fromA to A
e
. Norms onA
e
that extend the given complete norm ∥ · ∥ onA are investigated. The operator seminorm ∥ · ∥op onA
e
defined by ∥ · ∥ is a norm (resp. a complete norm) iffA has trivial left annihilator (resp. ∥ · ∥op restricted toA is equivalent to ∥ · ∥). 相似文献
3.
We review recent results on congruence lattices of (infinite) lattices. We discuss results obtained with box products, as
well as categorical, ring-theoretical, and topological results.
Received March 13, 2002; accepted in final form September 24, 2002.
RID="h1"
ID="h1" 相似文献
4.
Nicolae Danet 《Proceedings of the American Mathematical Society》2001,129(2):539-542
If and are Banach lattices such that is separable and has the countable interpolation property, then the space of all continuous regular operators has the Riesz decomposition property. This result is a positive answer to a conjecture posed by A. W. Wickstead.
5.
6.
A subclass of the class of dense lattices, called strongly dense lattices, is defined and its properties investigated. In
particular, an invariant of strongly dense lattices is defined and shown to take all possible values. Connections to module
theory are explored, including some constructions of von Neumann regular rings with strongly dense lattices of two-sided ideals.
Received September 16, 1997; accepted in final form July 22, 1998. 相似文献
7.
Representations of distributive semilattices in ideal lattices of various algebraic structures 总被引:2,自引:0,他引:2
We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000. 相似文献
8.
关于全不变扩张环和模(英文) 总被引:2,自引:0,他引:2
In this paper, we discuss FI-extending property of rings and modules. The main results are the following: a characterization of von Neumann regular rings which are two-sided FI-extending is given; sufficient conditions for direct summands of FI-extending modules to be FI-extending are obtained; and at last, a necessary and sufficient condition for nonsingular modules over nonsingular rings to be FI-extending is given. 相似文献
9.
In this paper we investigate when various Banach algebras associated to a locally compact group G have the weak or weak∗ fixed point property for left reversible semigroups. We proved, for example, that if G is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms, then the Fourier-Stieltjes algebra of G has the weak∗ fixed point property for left reversible semigroups if and only if G is compact. This generalizes a classical result of T.C. Lim for the case when G is the circle group T. 相似文献