共查询到20条相似文献,搜索用时 281 毫秒
1.
Peter Danchev 《Proceedings of the American Mathematical Society》2002,130(7):1937-1941
Let be an abelian group and let be a field of 0$">. It is shown via a universal algorithm that if the modified Direct-Factor Problem holds, then the -isomorphism for some group yields provided is a closed -group or a -local algebraically compact group. In particular, this is the case when is closed -primary of arbitrary power, or is -local algebraically compact with cardinality at most and is in cardinality not exceeding . The last claim completely settles a question raised by W. May in Proc. Amer. Math. Soc. (1979) and partially extends our results published in Rend. Sem. Mat. Univ. Padova (1999) and Southeast Asian Bull. Math. (2001).
2.
Daciberg L. Gonç alves Jan Jaworowski Pedro L. Q. Pergher 《Proceedings of the American Mathematical Society》2002,130(10):3111-3115
Let be a finite group acting freely in a CW-complex which is a homotopy -dimensional sphere and let be a map of to a finite -dimensional CW-complex . We show that if , then has an -coincidence for some nontrivial subgroup of .
3.
Tiberiu Dumitrescu Muhammad Zafrullah 《Proceedings of the American Mathematical Society》2002,130(6):1639-1644
Let be a saturated multiplicative set of an integral domain . Call an lcm splitting set if and are principal ideals for every and . We show that if is an -stable overring of (that is, if whenever and is principal, it follows that and if is an lcm splitting set of , then the saturation of in is an lcm splitting set in . Consequently, if is Noetherian and is a (nonzero) prime element, then is also a prime element of the integral closure of . Also, if is Noetherian, is generated by prime elements of and if the integral closure of is a UFD, then so is the integral closure of .
4.
Let be a complete local domain containing the integers with maximal ideal such that is at least the cardinality of the real numbers. Let be a nonmaximal prime ideal of such that is a regular local ring. We construct an excellent local ring such that the completion of is , the generic formal fiber of is local with maximal ideal and if is a nonzero ideal of , then is complete.
5.
Tapani Hyttinen Saharon Shelah 《Proceedings of the American Mathematical Society》2002,130(10):2837-2843
For suitable groups we will show that one can add a Boolean algebra by forcing in such a way that is almost isomorphic to . In particular, we will give a positive answer to the following question due to J. Roitman: Is a possible number of automorphisms of a rich Boolean algebra?
6.
M. Berkani 《Proceedings of the American Mathematical Society》2002,130(6):1717-1723
The aim of this paper is to show that if and are commuting B-Fredholm operators acting on a Banach space , then is a B-Fredholm operator and , where means the index. Moreover if is a B-Fredholm operator and is a finite rank operator, then is a B-Fredholm operator and We also show that if is isolated in the spectrum of , then is a B-Fredholm operator of index if and only if is Drazin invertible. In the case of a normal bounded linear operator acting on a Hilbert space , we obtain a generalization of a classical Weyl theorem. 相似文献
7.
Rü diger Gö bel Saharon Shelah 《Proceedings of the American Mathematical Society》2002,130(3):673-674
If and are groups and is a normal subgroup of , then the -closure of in is the normal subgroup of . In particular, is the -radical of . Plotkin calls two groups and geometrically equivalent, written , if for any free group of finite rank and any normal subgroup of the -closure and the -closure of in are the same. Quasi-identities are formulas of the form for any words in a free group. Generally geometrically equivalent groups satisfy the same quasi-identities. Plotkin showed that nilpotent groups and satisfy the same quasi-identities if and only if and are geometrically equivalent. Hence he conjectured that this might hold for any pair of groups. We provide a counterexample.
8.
Alireza Abdollahi Gunnar Traustason 《Proceedings of the American Mathematical Society》2002,130(10):2827-2836
For a given positive integer and a given prime number , let be the integer satisfying . We show that every locally finite -group, satisfying the -Engel identity, is (nilpotent of -bounded class)-by-(finite exponent) where the best upper bound for the exponent is either or if is odd. When the best upper bound is or . In the second part of the paper we focus our attention on -Engel groups. With the aid of the results of the first part we show that every -Engel -group is soluble and the derived length is bounded by some constant.
9.
H. F. Kreimer 《Proceedings of the American Mathematical Society》2002,130(10):2853-2856
Let be a Hopf algebra over a commutative ring such that is a finitely generated, projective module over , let be a right -comodule algebra, and let be the subalgebra of -coinvariant elements of . If is a Galois extension of and is a local subalgebra of the center of , then is a cleft right -comodule algebra or, equivalently, there is a normal basis for over .
10.
Let be a polynomial whose Julia set is locally connected. Then a non-preperiodic non-precritical vertex of must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of . In particular, if all critical points of are non-recurrent then all vertices of are preperiodic or precritical.
11.
N. Brodskiy J. Dydak A. Karasev K. Kawamura 《Proceedings of the American Mathematical Society》2007,135(2):587-596
Let be a Hausdorff compact space and let be the algebra of all continuous complex-valued functions on , endowed with the supremum norm. We say that is (approximately) -th root closed if any function from is (approximately) equal to the -th power of another function. We characterize the approximate -th root closedness of in terms of -divisibility of the first Cech cohomology groups of closed subsets of . Next, for each positive integer we construct an -dimensional metrizable compactum such that is approximately -th root closed for any . Also, for each positive integer we construct an -dimensional compact Hausdorff space such that is -th root closed for any .
12.
Let be a field and suppose that is irreducible in . We discuss the following question: under what conditions are all iterates of irreducible over ?
13.
Marius Mitrea 《Proceedings of the American Mathematical Society》2002,130(9):2599-2607
Let be a second order, (variable coefficient) elliptic differential operator and let , , 0$">, satisfy in the Lipschitz domain . We show that can exhibit more regularity on Besov scales for which smoothness is measured in with . Similar results are valid for functions representable in terms of layer potentials.
14.
Roman Dwilewicz Joë l Merker 《Proceedings of the American Mathematical Society》2002,130(7):1975-1980
Let be a compact, connected, -smooth and globally minimal hypersurface in which divides the projective space into two connected parts and . We prove that there exists a side, or , such that every continuous CR function on extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.
15.
Let be a division ring and let be a finite-dimensional -vector space, viewed multiplicatively. If is the multiplicative group of , then acts on and hence on any group algebra . Our goal is to completely describe the semiprime -stable ideals of . As it turns out, this result follows fairly easily from the corresponding results for the field of rational numbers (due to Brookes and Evans) and for infinite locally-finite fields. Part I of this work is concerned with the latter situation, while Part II deals with arbitrary division rings.
16.
Alexander Blokh Adam Fieldsteel 《Proceedings of the American Mathematical Society》2002,130(12):3571-3578
We characterize those subsets of the positive integers with the property that, whenever a point in a dynamical system enters a compact set along , contains a recurrent point. We do the same for uniform recurrence.
17.
Bryan Clair Shahriar Mokhtari-Sharghi 《Proceedings of the American Mathematical Society》2002,130(7):1881-1886
The -zeta function of an infinite graph (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by , the normalized zeta functions of the finite graphs converge to the -zeta function of .
18.
Riccardo Ghiloni 《Proceedings of the American Mathematical Society》2002,130(12):3525-3535
For each compact smooth manifold containing at least two points we prove the existence of a compact nonsingular algebraic set and a smooth map such that, for every rational diffeomorphism and for every diffeomorphism where and are compact nonsingular algebraic sets, we may fix a neighborhood of in which does not contain any regular rational map. Furthermore is not homotopic to any regular rational map. Bearing in mind the case in which is a compact nonsingular algebraic set with totally algebraic homology, the previous result establishes a clear distinction between the property of a smooth map to represent an algebraic unoriented bordism class and the property of to be homotopic to a regular rational map. Furthermore we have: every compact Nash submanifold of containing at least two points has not any tubular neighborhood with rational retraction.
19.
Hong Bing Yu 《Proceedings of the American Mathematical Society》2002,130(6):1623-1627
We give a generalization of Bleicher's result on signed sums of th powers. Let be an integral-valued polynomial of degree satisfying the necessary condition that there exists no integer 1$"> dividing the values for all integers . Then, for every positive integer and every integer , there are infinitely many integers and choices of such that
20.
J. Hagler 《Proceedings of the American Mathematical Society》2002,130(11):3313-3324
Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .