Some remarks on algebras with straightening laws

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Straightening Laws on Modules and Their Symmetric Algebras

Several modules M over algebras with straightening law A have a structure which is similar to the structure of A itself: M has a system of generators endowed with a natural partial order, a standard basis over the ring B of coefficients, and the multiplication A × M → A satisfies a “straightening law”. We call them modules with straightening law, briefly MSLs. In section 1 we recall the notion ...

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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 ...

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ژورنال

عنوان ژورنال: Journal of Pure and Applied Algebra

سال: 1994

ISSN: 0022-4049

DOI: 10.1016/0022-4049(94)90120-1