Generalized symmetric elements generated by a prime sequence |
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Authors: | M E Detlefsen |
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Institution: | (1) Department of Mathematics, Slippery Rock University, 229 Vincent Science Hall, Slippery Rock, PA 16057-1326, USA. E-mail: michael.detlefsen@sru.edu, US |
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Abstract: | Let be a prime sequence in a local Noether lattice L. For denotes the set of finite joins in L of power products of the generalized symmetric elements of order k (majorization elements) in together with 0 and I. We have previously showed that for is a Noetherian distributive
-domain. For and for any is again such a sub--domain of . For and is not closed under the meet of . However with its induced meet is again a Noetherian distributive -domain. Each finite set of majorization elements asymptotically forms a distributive sublattice of for k sufficiently large.
Received March 2, 1998; accepted in final form June 11, 1998. |
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Keywords: | and phrases: Noether lattice majorization prime sequence generalized symmetric elements |
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