On the discrete counterparts of Cohen-Macaulay algebras with straightening laws
نویسنده
چکیده
We study properties of a poset generating a Cohen-Macaulay algebra with straightening laws (ASL for short). We show that if a poset P generates a Cohen-Macaulay ASL, then P is pure and, if P is moreover Buchsbaum, then P is Cohen-Macaulay. Some results concerning a Rees algebra of an ASL defined by a straightening closed ideal are also established. And it is shown that if P is a Cohen-Macaulay poset with unique minimal element and Q is a poset ideal of P , then P ⊎Q is also Cohen-Macaulay. MSC: Primary: 13F50 Secondary: 13H10; 13F55; 13P10; 13C15
منابع مشابه
f-vectors and h-vectors of simplicial posets
Stanely, R.P., f-vectors and h-vectors of simplicial posets, Journal of Pure and Applied Algebra 71 (1991) 319-331. A simplicial poset is a (finite) poset P with d such that every interval [6, x] is a boolean algebra. Simplicial posets are generalizations of simplicial complexes. The f-vector f(P) = (f,, f,, , ,f_,) of a simplicial poset P of rank d is defined by f; = #{x E P: [6, x] g B,, I}, ...
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