Essential and inessential elements of a standard basis |
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Authors: | Giannina Beccari |
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Institution: | Dipartimento di Matematica, Politecnico Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy |
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Abstract: | In this paper we introduce the concept of inessential element of a standard basis B(I), where I is any homogeneous ideal of a polynomial ring. An inessential element is, roughly speaking, a form of B(I) whose omission produces an ideal having the same saturation as I; it becomes useless in any dehomogenization of I with respect to a linear form. We study the properties of B(I) linked to the presence of inessential elements and give some examples. |
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Keywords: | Primary 13A02 Secondary 13D40 13C99 |
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