Abstract
A finite poset Q is called integral over a field k if there exists an ASL (algebra with straightening laws) domain on Q∪{−∞} over k. We classify all ‘trees’ (rank one connected posets without cycles) which are integral over an infinite field.
AMS subject classifications (1980)
Primary 06A10 secondary 13H10Key words
Poset tree integral poset algebra with straightening lawsPreview
Unable to display preview. Download preview PDF.
References
- 1.D. Eisenbud (1980) Introduction to algebras with straightening laws, Ring Theory and Algebra III, Proc. Third Oklahoma Conf. (B. R. McDonald, ed.), Lecture Notes in Pure and Appl. Math., No. 55, Dekker, New York, pp. 243–268.Google Scholar
- 2.T. Hibi (1985) Distributive lattices, affine semigroup rings and algebras with straightening laws, to appear in Proc. USA-Japan Workshop on Commutative Algebra and Combinatorics (M. Nagata, ed.), Advanced Studies in Pure Math., Vol. 11, North-Holland, Amsterdam.Google Scholar
- 3.T. Hibi (1986) Level rings and algebras with straightening laws, submitted.Google Scholar
- 4.T. Hibi and K.-i. Watanabe (1985) Study of three-dimensional algebras with straightening laws which are Gorenstein domains I, Hiroshima Math. J. 15, 27–54.Google Scholar
- 5.K.-i. Watanabe (1986) Study of four-dimensional Gorenstein ASL domains, I (Integral posets arising from triangulations of a 2-sphere), to appear in Proc. USA-Japan Workshop on Commutative Algebra and Combinatorics (M. Nagata, ed.), Advanced Studies in Pure Math., Vol. 11, North-Holland, Amsterdam.Google Scholar
Copyright information
© D. Reidel Publishing Company 1987