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391.
本文引入一类非结合泛代数,即零积结合近环,研究其次直积分解,得到两个结构定理。设N是零积结合分配生成近环,本文证明了:(i)如果N是次直不可约的且无非零的二次幂零元,则N是整的;(ii)N是零积结合分配生成整近环的次直积当且仅当N不含非零的二次幂零元。这些结果在这一类泛代数中加强了著名的Birkhoff定理。 相似文献
392.
F. Wehrung 《Transactions of the American Mathematical Society》2004,356(5):1957-1970
We find a distributive -semilattice of size that is not isomorphic to the maximal semilattice quotient of any Riesz monoid endowed with an order-unit of finite stable rank. We thus obtain solutions to various open problems in ring theory and in lattice theory. In particular:
- --
- There is no exchange ring (thus, no von Neumann regular ring and no C*-algebra of real rank zero) with finite stable rank whose semilattice of finitely generated, idempotent-generated two-sided ideals is isomorphic to .
- --
- There is no locally finite, modular lattice whose semilattice of finitely generated congruences is isomorphic to .
393.
Marek?Hy?ko Mirko?NavaraEmail author 《International Journal of Theoretical Physics》2005,44(12):2239-2248
We discuss the possibility of automatic simplification of formulas in orthomodular lattices. We describe the principles of
a program which decides the validity of equalities and inequalities, as well as implications between them and other important
relations significant in quantum mechanics.
PACS: 02.10.-v, 02.10.Ab, 02.10.De, 03.65.Fd.
AMS Subject classification: 06C15, 03G12, 06B10, 06B25, 81P10. 相似文献
394.
It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity of equivalence terms and several other 3-variable expressions involving equivalence terms have been proved to hold in any orthomodular lattice. Symmetric differences have been shown to reduce to complements of equivalence terms. Some congruence relations related to equivalence operations and symmetric differences have been considered. 相似文献
395.
Deguang Han 《Proceedings of the American Mathematical Society》2003,131(1):275-284
Interpolation operators associated with wavelets sets introduced by Dai and Larson play an important role in their operator algebraic approach to wavelet theory. These operators are also related to the von Neumann subalgebras in the ``local commutant' space, which provides the parametrizations of wavelets. It is a particularly interesting question of how to construct operators which are in the local commutant but not in the commutant. Motivated by some questions about interpolation family and C*-algebras in the local commutant, we investigate the interpolation partial isometry operators induced by sub-frame sets. In particular we introduce the -congruence domain of the associated mapping between two sub-frame sets and use it to characterize these partial isometries in the local commutant. As an application, we obtain that if two wavelet sets have the same -congruence domain, then one is a multiresolution analysis (MRA) wavelet set which implies that the other is also an MRA wavelet set.
396.
We use the theory of quadratic base change to derive some new identities involving the Ramanujan -function, and show how the Ramanujan congruence (n) 11(n) (mod 691) follows. 相似文献
397.
Let
be a group of affine transformations of the plane that contains a strict contraction and all translations. It is shown that
any two topological discs
are congruent dissection with respect to
such that only three topological discs are used as pieces of dissection. Two pieces of dissection do not suffice in general
even if
consists of all affine transformations.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
398.
399.
Andrei A. Krokhin 《Order》2001,18(2):151-159
We continue the study of congruences of clone lattices
A
, where A is finite, started in an earlier paper by the author and A. P. Semigrodskikh. We prove that each clone that either contains all unary operations or consists of essentially unary operations forms a one-element class of any non-trivial congruence of
A
. As a consequence, we get that
A
has the greatest non-trivial congruence provided the lattice is not simple, that
A
is directly indecomposable, and that it has neither distributive nor dually distributive elements except for the trivial ones.For |A|>2, no example of a non-trivial congruence is known so far. We exhibit some reasons why such congruences are not easy to find. 相似文献
400.
Andrzej Walendziak 《Czechoslovak Mathematical Journal》2004,54(1):155-160
In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images. 相似文献