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221.
张跃辉 《中国科学A辑(英文版)》2002,45(6):741-748
Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra
T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the
maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of
A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if
and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the
exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there
exists an idempotent e of A, and an invertible element u of A, such that eBe = u-1eCeu. 相似文献
222.
R. Hazrat 《Proceedings of the American Mathematical Society》2002,130(2):311-314
This article provides a short and elementary proof of the key theorem of reduced -theory, namely Platonov's Congruence theorem. Our proof is based on Wedderburn's factorization theorem.
223.
Thierry Levasseur 《Proceedings of the American Mathematical Society》2002,130(12):3519-3523
Let be a complex semisimple Lie algebra and be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of is equal to the dimension of a Borel subalgebra of .
224.
Saharon Shelah Juris Steprans 《Proceedings of the American Mathematical Society》2002,130(7):2097-2106
Martin's Axiom does not imply that all automorphisms of are somewhere trivial. An alternate method for obtaining models where every automorphism of is somewhere trivial is explained.
225.
Andrei S. Rapinchuk Yoav Segev Gary M. Seitz 《Journal of the American Mathematical Society》2002,15(4):929-978
We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let be a finite dimensional division algebra having center , and let be a normal subgroup of finite index. Suppose is not solvable. Then we may assume that is a minimal nonsolvable group (MNS group for short), i.e. a nonsolvable group all of whose proper quotients are solvable. Our proof now has two main ingredients. One ingredient is to show that the commuting graph of a finite MNS group satisfies a certain property which we denote Property . This property includes the requirement that the diameter of the commuting graph should be , but is, in fact, stronger. Another ingredient is to show that if the commuting graph of has Property , then is open with respect to a nontrivial height one valuation of (assuming without loss of generality, as we may, that is finitely generated). After establishing the openness of (when is an MNS group) we apply the Nonexistence Theorem whose proof uses induction on the transcendence degree of over its prime subfield to eliminate as a possible quotient of , thereby obtaining a contradiction and proving our main result.
226.
Jonathan A. Scott 《Transactions of the American Mathematical Society》2002,354(8):3075-3084
Let be a finite, -dimensional, -connected CW complex. We prove the following theorem:
If is an odd prime, then the loop space homology Bockstein spectral sequence modulo is a spectral sequence of universal enveloping algebras over differential graded Lie algebras.
227.
Anatolij Dvurečenskij 《International Journal of Theoretical Physics》2002,41(12):2311-2318
We show that every effect algebra satisfying the Riesz decomposition property can be represented as an effect algebra of automorphisms of an antilattice, and every MV-algebra can be represented as an MV-algebra of automorphisms of a linearly ordered set. Such a representation enables us to visualize effect algebras by functions. This is a variation of the Holland representation theorem for -groups and of its generalization of Glass for directed interpolation po-groups as -groups or po-groups automorphisms of linearly ordered set or of an antilattice, respectively. 相似文献
228.
Ch. F. D. McCoy 《Algebra and Logic》2002,41(5):295-305
The notion of
3
0
-categoricity in linear orderings and Boolean algebras is examined. We provide a proof for the fact that there are uncountably many relatively
3
0
-categorical linear orderings, and furnish a proof of another fact which suggests that the (unrelatively)
3
0
-categorical linear orderings may be very difficult to classify. In stark contrast to these results for linear orderings, a complete classification of the relatively
3
0
-categorical Boolean algebras is given. 相似文献
229.
Roman Frič 《Czechoslovak Mathematical Journal》2002,52(4):861-874
We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets. 相似文献
230.
We list characters (one-dimensional representations) of the reflection equation algebra associated with the fundamental vector representation of the Drinfeld–Jimbo quantum group
q
(gl(n)). 相似文献