Bases for the positive cone of a partially ordered module
Author:
W. Russell Belding
Journal:
Trans. Amer. Math. Soc. 235 (1978), 305-313
MSC:
Primary 06A75
DOI:
https://doi.org/10.1090/S0002-9947-1978-0472640-8
MathSciNet review:
0472640
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Abstract | References | Similar Articles | Additional Information
Abstract: is a partially ordered ring and
is a strict
-module. So M is a left R-module and
. Let
be the order induced on M by
is an
-basis for
means
(spanning) and if r is in R, b in B with
then
(independence).
Result: If B and D are -bases for
then card
card D and to within a permutation
, for units
of
.
- [1] M. N. Bleicher and E. Marczewski, Remarks on dependence relations and closure operators, Colloq. Math. 9 (1962), 209-212. MR 26 #58. MR 0142489 (26:58)
- [2] M. N. Bleicher and H. Schneider, The decomposition of cones in modules over ordered rings, J. Algebra 1 (1964), 233-258. MR 29 #5866. MR 0168606 (29:5866)
- [3] P. M. Cohn, Universal algebra, Harper and Row, New York, 1965. MR 31 #224; erratum 32, p. 1754. MR 0175948 (31:224)
- [4] L. Fuchs, Partially ordered algebraic systems, Addison-Wesley, Reading, Mass., 1963. MR 30 #2090. MR 0171864 (30:2090)
- [5] G. A. Heuer, Discrete ordered rings, Fund. Math. 85 (1974), no. 2 121-138. MR 49 #8915. MR 0344175 (49:8915)
- [6] N. Jacobson, Lectures in abstract algebra. II, Van Nostrand, Princeton, N.J., 1953. MR 14, 837. MR 0053905 (14:837e)
- [7] P. Ribenboim, On ordered modules, J. Reine Angew. Math. 225 (1967), 120-146. MR 34 #5877. MR 0206052 (34:5877)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1978-0472640-8
Keywords:
Partially ordered ring,
partially ordered module,
directed,
order preserving automorphism group,
closure operator
Article copyright:
© Copyright 1978
American Mathematical Society