共查询到10条相似文献,搜索用时 93 毫秒
1.
Larry Smith 《Proceedings of the American Mathematical Society》2003,131(4):1043-1048
Let be a representation of a finite group over the field . Denote by the algebra of polynomial functions on the vector space . The group acts on and hence also on . The algebra of coinvariants is , where is the ideal generated by all the homogeneous -invariant forms of strictly positive degree. If the field has characteristic zero, then R. Steinberg has shown (this is the formulation of R. Kane) that is a Poincaré duality algebra if and only if is a pseudoreflection group. In this note we explore the situation for fields of nonzero characteristic. We prove an analogue of Steinberg's theorem for the case and give a counterexample in the modular case when .
2.
Saugata Basu Richard Pollack Marie-Franç oise Roy 《Proceedings of the American Mathematical Society》2005,133(4):965-974
Let be a real closed field and let and be finite subsets of such that the set has elements, the algebraic set defined by has dimension and the elements of and have degree at most . For each we denote the sum of the -th Betti numbers over the realizations of all sign conditions of on by . We prove that
This generalizes to all the higher Betti numbers the bound on . We also prove, using similar methods, that the sum of the Betti numbers of the intersection of with a closed semi-algebraic set, defined by a quantifier-free Boolean formula without negations with atoms of the form or for , is bounded by
making the bound more precise.
This generalizes to all the higher Betti numbers the bound on . We also prove, using similar methods, that the sum of the Betti numbers of the intersection of with a closed semi-algebraic set, defined by a quantifier-free Boolean formula without negations with atoms of the form or for , is bounded by
making the bound more precise.
3.
Matej Bresar Ajda Fosner Peter Semrl 《Proceedings of the American Mathematical Society》2003,131(12):3833-3837
Let be be semisimple Banach algebras and let be a unital bijective linear operator that preserves invertibility. If the socle of is an essential ideal of , then is a Jordan isomorphism.
4.
Ulrich Albrecht 《Proceedings of the American Mathematical Society》2003,131(4):1021-1029
This paper investigates the extent to which an Abelian group is determined by the homomorphism groups . A class of Abelian groups is a Fuchs 34 class if and in are isomorphic if and only if for all . Two -groups and satisfy for all groups if and only if they have the same -Ulm-Kaplansky-invariants and the same final rank. The mixed groups considered in this context are the adjusted cotorsion groups and the class introduced by Glaz and Wickless. While is a Fuchs 34 class, the class of (adjusted) cotorsion groups is not. 相似文献
5.
Dong Zhe 《Proceedings of the American Mathematical Society》2005,133(6):1629-1637
In this paper we prove that for any unital -weakly closed algebra which is -weakly generated by finite-rank operators in , every -weakly closed -submodule has . In the case of nest algebras, if are nests, we obtain the following -fold tensor product formula:
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
6.
Nuria Corral Percy Ferná ndez-Sá nchez 《Proceedings of the American Mathematical Society》2006,134(4):1125-1132
We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation of in terms of the Milnor number of . This result gives a bound for the degree of an algebraic invariant curve of a foliation of in terms of the degree of , provided that all the branches of are isolated separatrices.
7.
Natasha Dobrinen 《Proceedings of the American Mathematical Society》2003,131(1):309-318
The games and are played by two players in -complete and max -complete Boolean algebras, respectively. For cardinals such that or , the -distributive law holds in a Boolean algebra iff Player 1 does not have a winning strategy in . Furthermore, for all cardinals , the -distributive law holds in iff Player 1 does not have a winning strategy in . More generally, for cardinals such that , the -distributive law holds in iff Player 1 does not have a winning strategy in . For regular and , implies the existence of a Suslin algebra in which is undetermined.
8.
M'hammed El Kahoui 《Proceedings of the American Mathematical Society》2004,132(9):2537-2541
A well-known theorem, due to Nagata and Nowicki, states that the ring of constants of any -derivation of , where is a commutative field of characteristic zero, is a polynomial ring in one variable over . In this paper we give an elementary proof of this theorem and show that it remains true if we replace by any unique factorization domain of characteristic zero.
9.
Krzysztof Plotka 《Proceedings of the American Mathematical Society》2003,131(4):1031-1041
We say that a function is a Hamel function ( ) if , considered as a subset of , is a Hamel basis for . We prove that every function from into can be represented as a pointwise sum of two Hamel functions. The latter is equivalent to the statement: for all there is a such that . We show that this fails for infinitely many functions.
10.
Gerd Zeibig 《Proceedings of the American Mathematical Society》2003,131(8):2491-2500
Given two locally compact spaces and a continuous map the Banach lattice is naturally a -module. Following the Bourbaki approach to integration we define generalized measures as -linear functionals . The construction of an -space and the concepts of absolute continuity and density still make sense. However we exhibit a counter-example to the natural generalization of the Radon-Nikodym Theorem in this context.