Publication Date

7-8-1974

Abstract

Let R be the ring of polynomials in a denumerable set of independent indeterminates over a field F and let I be an ideal (Xo,x1,x2, ... ) in R. A Levi structure for I provides bases for I and R as vector spaces over F and an associated algorithm for determining whether an element of R is in I.

Such structures have been developed previously for certain principal differential ideals [i.e., ideals (Xc),x1 , ... ) with xj the j-th derivative of Xol in which the generator is homogeneous and isobaric and for a family of related ordinary ideals. The present paper extends this to cases in which the generator need not be homogeneous and need not be isobaric and also presents Levi structures for ideals generated by subsets of the xj. The family of ordinary ideals is enlarged similarly.

These generalizations are obtained with the aid of a new ordering of power products in the indeterminates. In particular, a Levi structure is given for the differential ideal [zg] generated by the g-th derivative of the product z = y1y2...yn of n independent differential indeterminates.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Abraham P. Hillman

Second Committee Member

Gustave A. Efroymson

Third Committee Member

Donald Ward Dubois

Language

English

Document Type

Dissertation

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