In this paper, we consider a monomial ideal J / P := A[x1, . . . , xn], over a commutative ring A, and we face the problem of the characterization for the familyMf (J) of all homogeneous ideals I / P such that the A-module P/I is free with basis given by the set of terms in the Gröbner escalier N(J) of J. This family is in general wider than that of the ideals having J as initial ideal w.r.t. a...

It is a common trend in mathematics to study (natural) dualities for general algebraic structures and, in particular, for those arising from mathematical logic. The first step towards this direction traces back to the pioneering work by Stone for Boolean algebras [12]. Later on, Stone duality has been extended to the more general case of distributive lattices by Priestley [8], [9]. The two abov...

A self-dual map $G$ is said to be \emph{antipodally self-dual} if the dual $G^*$ antipodal embedded in $\mathbb{S}^2$ with respect $G$. In this paper, we investigate necessary and/or sufficient conditions for a antipodally self-dual. particular, present combinatorial characterization terms of certain \emph{involutive labelings}. The latter lead us obtain \emph{strongly involutive} (a notion rel...

We revisit the problem of consistent free propagation higher-spin fields in nontrivial backgrounds, focusing on symmetric tensor(-spinor)s. The Fierz-Pauli equations for massive flat space form an involutive system, whose algebraic consistency owes to certain gauge identities. zero mass limit former leads directly massless transverse-traceless gauge, where both field and parameter have their re...

Inspired by the work of Chevalley and Eilenberg on de Rham cohomology compact Lie groups, we prove that, under certain algebraic topological conditions, associated to left-invariant elliptic, even hypocomplex, involutive structures groups can be computed using only algebras, thus reducing analytical problem a purely one. The main tool is Leray spectral sequence that connects result obtained Bot...