This paper was adopted by the CJLS on December 12, 1990 by a vote of eleven in favor, two opposed, and five abstaining ( 11-2-5). Members voting in favor: Rabbis Kassel Abelson, Ben Zion Bergman, Elliot N. Dorff, Amy Eilberg, Dov Peretz Elkins, Howard Handler, Reuven Kimelman, Lionel E. Moses, Mayer E. Rabinowitz, Joel Rembaum, Morris M. Shapiro. Members voting against: Rabbis Avram I. Reisner ...

This paper was adopted by the CJLS on December 12, 1990 by a vote of thirteen infavor, one opposed, andfour abstaining (13-1-4). Members voting in favor: Rabbis Ben Zion Bergman, Stanley Bramnick, Jerome M. Epstein, David M. Feldman, Sam Fraint, Howard Handler, Reuven Kimelman, Herbert Mandl, Lionel E. Moses, Mayer E. Rabinowitz, Avram I. Reisner, Joel Rembaum, Joel Roth. Member voting against:...

A weaker form of the multiplicity conjecture of Herzog, Huneke, and Srinivasan is proven for two classes of monomial ideals: quadratic monomial ideals and squarefree monomial ideals with sufficiently many variables relative to the Krull dimension. It is also shown that tensor products, as well as Stanley-Reisner ideals of certain unions, satisfy the multiplicity conjecture if all the components...

In 1974, the author proved that codimension of ideal (g1,g2,…,gd) generated in group algebra K[Zd] over a field K characteristic 0 by generic Laurent polynomials having same Newton polytope Γ is equal to d!×Volume(Γ). Assuming Newtons simplicial and super-convenient (that is, containing some neighborhood origin), strengthens 1974 result explicitly specifying set Bsh monomials cardinality d!×Vol...

We show that a finite regular cell complex with the intersection property is a Cohen-Macaulay space iff the top enriched cohomology module is the only nonvanishing one. We prove a comprehensive generalization of Balinski’s theorem on convex polytopes. Also we show that for any Cohen-Macaulay cell complex as above, although there is now generalization of the Stanley-Reisner ring of simplicial co...

Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...

Generalizing the notion of a Koszul algebra, a graded kalgebra A is K2 if its Yoneda algebra ExtA(k, k) is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem about K2 factor algebras of Koszul algebras and use that theorem to show the Stanley-Reisner face ring of a simplicial complex ∆ is K2 whenever the Alexander dual simplicial complex ∆∗ is (sequentially) Cohen-...