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1.
D. Daigle 《Proceedings of the American Mathematical Society》1996,124(5):1337-1345
Let be a field of characteristic and a polynomial algebra in two variables. By a -generator of we mean an element of for which there exist and such that . We also define a -line of to mean any element of whose coordinate ring is that of a -generator. Then we prove that if is such that is a -line of (where is an indeterminate over ), then is a -generator of . This is analogous to the well-known fact that if is such that is a line of , then is a variable of . We also prove that if is a -line of for which there exist and such that , then is in fact a -generator of .
2.
David Handel 《Proceedings of the American Mathematical Society》1996,124(5):1609-1613
A continuous map is said to be -regular if whenever are distinct points of , then are linearly independent over . For smooth manifolds we obtain new lower bounds on the minimum for which a -regular map can exist in terms of the dual Stiefel-Whitney classes of .
3.
Sam Huckaba 《Proceedings of the American Mathematical Society》1996,124(5):1393-1401
A -dimensional version is given of a -dimensional result due to C. Huneke. His result produced a formula relating the length to the difference , where is primary for the maximal ideal of a -dimensional Cohen-Macaulay local ring , is a minimal reduction of , , and is the Hilbert-Samuel polynomial of . We produce a formula that is valid for arbitrary dimension, and then use it to establish some formulas for the Hilbert coefficients of . We also include a characterization, in terms of the Hilbert coefficients of , of the condition .
4.
Robert Sandling 《Proceedings of the American Mathematical Society》1996,124(5):1347-1350
It is shown that the isomorphism type of a metacyclic -group is determined by its group algebra over the field of elements. This completes work of Baginski. It is also shown that, if a -group has a cyclic commutator subgroup , then the order of the largest cyclic subgroup containing is determined by .
5.
Let be the \u{C}ech-Stone remainder . We show that there exists a large class of images of such that whenever is a subset of of cardinality at most the continuum, then is again an image of . The class contains all separable compact spaces, all compact spaces of weight at most and all perfectly normal compact spaces.
6.
P. M. Gadea J. Muñ oz Masqué 《Proceedings of the American Mathematical Society》1996,124(5):1437-1443
Let be a finite-dimensional commutative algebra over and let , and be the ring of -differentiable functions of class , the ring of real analytic mappings with values in and the ring of -analytic functions, respectively, defined on an open subset of . We prove two basic results concerning -differentiability and -analyticity: ) , ) if and only if is defined over .
7.
P. D. Johnson Jr. R. N. Mohapatra Jr. David Ross Jr. 《Proceedings of the American Mathematical Society》1996,124(2):543-547
Suppose is a non-increasing sequence of non-negative numbers with , , , and is the lower triangular matrix defined by , , and , . We show that the operator norm of as a linear operator on is no greater than , for ; this generalizes, yet again, Hardy's inequality for sequences, and simplifies and improves, in this special case, more generally applicable results of D. Borwein, Cass, and Kratz. When the tend to a positive limit, the operator norm of on is exactly . We also give some cases when the operator norm of on is less than .
8.
We first provide an example of a ring such that all possible structural matrix rings over are isomorphic. However, we prove that the underlying graphs of any two isomorphic structural matrix rings over a semiprime Noetherian ring are isomorphic, i.e. the underlying Boolean matrix of a structural matrix ring over a semiprime Noetherian ring can be recovered, contrary to the fact that in general cannot be recovered.
9.
To a given basis on an -dimensional Hilbert space , we associate the algebra of all linear operators on having every as an eigenvector. So, is commutative, semisimple, and -dimensional. Given two algebras of this type, and , there is a natural algebraic isomorphism of and . We study the question: When does preserve the operator norm?
10.
Christian Friesen Doug Hensley 《Proceedings of the American Mathematical Society》1996,124(9):2661-2673
Given a finite field of order and polynomials of degrees respectively, there is the continued fraction representation . Let denote the number of such pairs for which and for . We give both an exact recurrence relation, and an asymptotic analysis, for . The polynomial associated with the recurrence relation turns out to be of P-V type. We also study the distribution of . Averaged over all and as above, this presents no difficulties. The average value of is , and there is full information about the distribution. When is fixed and only is allowed to vary, we show that this is still the average. Moreover, few pairs give a value of that differs from this average by more than
11.
Let be a Banach space. For we prove that the identity map is -summing if and only if the operator is nuclear for every unconditionally summable sequence in , where is the conjugate number for . Using this result we find a characterization of Banach spaces in which every -weakly summable sequence lies inside the range of an -valued measure (equivalently, every -weakly summable sequence in , satisfying that the operator is compact, lies in the range of an -valued measure) with bounded variation. They are those Banach spaces such that the identity operator is -summing.
12.
It is proved that if are bounded -semigroups on Banach spaces and , resp., and , are bounded operators with dense ranges such that intertwines with and commutes with , then is strongly stable provided ---the generator of ---does not have eigenvalue on . An analogous result holds for power-bounded operators.
13.
Julius M. Zelmanowitz 《Proceedings of the American Mathematical Society》1996,124(10):2955-2960
If is an -faithful -module, then there is an order-preserving correspondence between the closed -submodules of and the closed -submodules of , where .
14.
Jodie D. Novak 《Proceedings of the American Mathematical Society》1996,124(3):969-975
For the Lie group , let be the open orbit of Lagrangian planes of signature in the generalized flag variety of Lagrangian planes in . For a suitably chosen maximal compact subgroup of and a base point we have that the orbit of is a maximal compact subvariety of . We show that for the connected component containing in the space of translates of which lie in is biholomorphic to , where denotes with the opposite complex structure.
15.
Dusan Repovs Arkadij B. Skopenkov Evgenij V. Scepin 《Proceedings of the American Mathematical Society》1996,124(4):1219-1226
We give the characterization of -homogeneous compacta in : Let be a locally compact (possibly nonclosed) subset of . Then is -homogeneous if and only if is a -submanifold of .
16.
Let be a locally compact group equipped with right Haar measure. The right differences of functions on are defined by for . Let and suppose for some and all . We prove that is a right uniformly continuous function of . If is abelian and the Beurling spectrum does not contain the unit of the dual group , then we show . These results have analogues for functions , where is a separable or reflexive Banach space. Finally, we apply our methods to vector-valued right uniformly continuous differences and to absolutely continuous elements of left Banach -modules.
17.
A probability measure on a product space is said to be bistochastic with respect to measures on and on if the marginals and are exactly and . A solution is presented to a problem of Arveson about sets which are of measure zero for all such .
18.
W. G. Dwyer S. Stolz L. R. Taylor 《Proceedings of the American Mathematical Society》1996,124(7):2235-2239
We prove the following theorem and some generalizations. . Let be a connected CW complex which satisfies Poincaré duality of dimension . For any subgroup of , let denote the cover of corresponding to . If has infinite index in , then is homotopy equivalent to an -dimensional CW complex.
19.
We prove that if a commutative semi-simple Banach algebra is the range of a ring homomorphism from a commutative -algebra, then is -equivalent, i.e. there are a commutative -algebra and a bicontinuous algebra isomorphism between and . In particular, it is shown that the group algebras , and the disc algebra are not ring homomorphic images of -algebras.
20.
Matthew Miller Rafael H. Villarreal 《Proceedings of the American Mathematical Society》1996,124(2):377-382
Assume is a polynomial ring over a field and is a homogeneous Gorenstein ideal of codimension and initial degree . We prove that the number of minimal generators of that are of degree is bounded above by , which is the number of minimal generators of the defining ideal of the extremal Gorenstein algebra of codimension and initial degree . Further, is itself extremal if .