A note on complete intersections

of height three

Author:
Junzo Watanabe

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3161-3168

MSC (1991):
Primary 13H05

DOI:
https://doi.org/10.1090/S0002-9939-98-04477-3

MathSciNet review:
1459155

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a field of characteristic 0. If is a complete intersection generated by three homogeneous elements of degrees with , then the reduction of by a general linear form is minimally generated by three elements if and only if .

**1.**D. A. Buchsbaum and D. Eisenbud,*Algebraic structures for finite free resolutions, and some structure theorem for ideals of codimension 3*, Amer. J. Math.**99**(1977), 447-485. MR**56:11983****2.**J. H. Grace and A. Young,*The algebra of invariants*, Cambridge Univ. Press, 1903.**3.**A. Iarrobino,*Associated graded algebra of a Gorenstein algebra*, Mem. Amer. Math. Soc.**107**1994. MR**94f:13009****4.**-,*Compressed algebras*, Trans. Amer. Math. Soc.**285**(1984), 337-378. MR**85j:13030****5.**J. Watanabe,*The Dilworth number of Artinian rings and finite posets with rank function*, Adv. Stud. Pure Math.**11**(1987), 303-312. MR**89k:13015****6.**-,*-Full ideals*, Nagoya Math. J.**106**(1987), 101-111. MR**88g:13003****7.**-,*A note on Gorenstein rings of embedding codimension three*, Nagoya Math. J.**50**(1973), 227-232.

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Additional Information

**Junzo Watanabe**

Email:
junzowat@ss.u-tokai.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-98-04477-3

Keywords:
Homogeneous Artinian algebra,
complete intersection,
weak Lefschetz condition

Received by editor(s):
July 11, 1996

Received by editor(s) in revised form:
March 28, 1997

Additional Notes:
This research was supported by Project C of Tokai University.

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1998
American Mathematical Society