Geodesic
The M\"obius inverse formulas on Abelian semigroups
Čebyševskij sbornik, Tome 10 (2009) no. 2, pp. 55-78

Voir la notice de l'article provenant de la source Math-Net.Ru

Let \(\Lambda\) be a commutative ring with identity element. Given a locally finite Abelian semigroup $X$ with identity element ${1\mspace{-4.85mu}{\mathrm I}}$ one may ask if the Möbius–type \(\Lambda\)–valued function exists on $X$. As it is proved in the present paper the existence of such a function often depends on the following property of $\zeta$–function of $X$: this function has not zeros $\chi$ such that the support of the character $\chi$ is a finite subset of $X$. \(\mathbb{Z}\)–valued Möbius function exists if and only if \(x^2=x\) implies \(x={1\mspace{-4.85mu}{\mathrm I}}\). Bibl. 12.
Keywords: Locally finite Abelian semigroup, ideal, idempotent, character, $\zeta$–functions, algebraic invertibility. 
@article{CHEB_2009_10_2_a2,
     author = {E. A. Gorin},
     title = {The {M\"obius} inverse formulas on {Abelian} semigroups},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {55--78},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a2/}
}
TY  - JOUR
AU  - E. A. Gorin
TI  - The M\"obius inverse formulas on Abelian semigroups
JO  - Čebyševskij sbornik
PY  - 2009
SP  - 55
EP  - 78
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a2/
LA  - ru
ID  - CHEB_2009_10_2_a2
ER  - 
%0 Journal Article
%A E. A. Gorin
%T The M\"obius inverse formulas on Abelian semigroups
%J Čebyševskij sbornik
%D 2009
%P 55-78
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a2/
%G ru
%F CHEB_2009_10_2_a2
E. A. Gorin. The M\"obius inverse formulas on Abelian semigroups. Čebyševskij sbornik, Tome 10 (2009) no. 2, pp. 55-78. http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a2/