In this paper, we discuss a few simple methods for computing the local topological index and its various analogs vector fields differential forms given on complex varieties with singularities of different types. They are based properties regular meromorphic logarithmic forms, dualizing (canonical) module related constructions. particular, show how to compute Cohen–Macaulay, Gorenstein monomial ...

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

We introduce left and right series of semi-braces. This allows to define nilpotent study the structure such semi-braces generalize some results, known for skew braces, B that set additive idempotents E is an ideal . Finally we concept a semi-brace show multiplicative group nilpotent.

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

Let X be a complex, smooth, complete and connected curve and G be a complex simple and simply connected algebraic group. We compute the Picard group of the stack of quasi-parabolic G-bundles over X, describe explicitly its generators in case for classical G and G 2 and then identify the corresponding spaces of global sections with the vacua spaces of Tsuchiya, Ueno and Yamada. The method uses t...

Any monotone Boolean function on a lattice can be described by the set of its minimal 1 values. If a lattice is given as a concept lattice, this set can be represented by the set of minimal hypotheses of a classification context. Enumeration of minimal hypotheses in output polynomial time is shown to be impossible unless P = NP, which shows that dualization of monotone functions on lattices wit...