We use the theory of poset resolutions to construct the minimal free resolution of an arbitrary stable monomial ideal in the polynomial ring whose coefficients are from a field. This resolution is recovered by utilizing a poset of Eliahou-Kervaire admissible symbols associated to a stable ideal. The structure of the poset under consideration is quite rich and in related analysis, we exhibit a r...

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero minimal fixed *-graded exponent if, and only generated by subalgebra an upper block triangular matrix algebra equipped suitable elementary ?2-grading involution.

We give an elementary description of the maps in the linear strand of the minimal free resolution of a square-free monomial ideal, that is, the Stanley-Reisner ideal associated to a simplicial complex. The description is in terms of the homology of the canonical Alexander dual complex. As applications we are able to prove for monomial ideals and j = 1 a conjecture of J. Herzog giving lower boun...

We discuss the linearity of the minimal free resolution of a power of an edge ideal.

Let v be a valuation of the quotient field of a noetherian local domain R. Assume that v is centered at R. This paper studies the structure of the value semigroup of v, S. Ideals defining toric varieties can be defined from the graded algebra K[T ] of cancellative commutative finitely generated semigroups such that T ∩ (−T ) = {0}. The value semigroup of a valuation S need not be finitely gener...

Let R=k[x1,…,xn] denote the standard graded polynomial ring over a field k. We study certain classes of equigenerated monomial ideals with property that so-called complementary ideal has no linear relations on generators. then use iterated trimming complexes to deduce Betti numbers for such ideals. Furthermore, using result splitting mapping cones by Miller and Rahmati, we construct minimal fre...