In prime characteristic there are important invariants that allow us to measure singularities. For certain cases, it is known they rational numbers. this article, we show property for Stanley-Reisner rings in several cases.

We show that the Stanley-Reisner ideal of the one-dimensional simplicial complex whose diagram is an n-gon is always a set-theoretic complete intersection in any positive characteristic.

We introduce a class of Stanley-Reisner ideals called generalized complete intersection, which is characterized by the property that all the residue class rings of powers of the ideal have FLC. We also give a combinatorial characterization of such ideals.

The first, fully non linear, mean field theory of relativistic gravitation has been developed in 2004. The theory makes the striking prediction that averaging or coarse graining a gravitational field changes the matter content of space-time. A review of the general theory is presented, together with new calculations that highlight this effect on black holes of the Reisner-Nordström (RN) family....

The strong ring R is a commutative ring generated by finite abstract simplicial complexes. To every G ∈ R belongs a Hodge Laplacian H = H(G) = D = (d + d∗)2 determining the cohomology and a unimodular connection operator L = L(G). The sum of the matrix entries of g = L−1 is the Euler characteristic χ(G). For any A,B ∈ R the spectra of H satisfy σ(H(A × B)) = σ(H(A)) + σ(H(B)) and the spectra of...

Abstract We study how some coefficients of two-variable coboundary polynomials can be derived from Betti numbers Stanley–Reisner rings. also explain the connection with these rings forces and Möbius to satisfy certain universal equations.

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.