caa a22 4500 445345241 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00233-011-9327-5 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9327-5 Commutative semigroups with cancellation law: a representation theorem [Elektronische Daten] [J. Grzybowski, D. Pallaschke, H. Przybycień, R. Urbański] Any commutative, cancellative semigroup S with 0 equipped with a uniformity can be embedded in atopological group $\widetilde{S}$ . We introduce the notion of semigroup symmetry T which enables us to turn $\widetilde{S}$ into an involutive group. In Theorem2.8 we prove that if S is 2-torsion-free and T is 2-divisible then the decomposition of elements of $\widetilde{S}$ into a sum of elements of the symmetric subgroup $\widetilde{S}_{s}$ and the asymmetric subgroup $\widetilde{S}_{a}$ is polar. In Theorem3.7 we give conditions under which atopological group $\widetilde{S}$ is atopological direct sum of its symmetric subgroup $\widetilde{S}_{s}$ and its asymmetric subgroup $\widetilde{S}_{a}$ . Theorem2.8 and Theorem3.7 are designed to be useful tools in studying Minkowski-Rådström-Hörmander spaces (and related topological groups $\widetilde{S}$ ), which are natural extensions of semigroups of bounded closed convex subsets of real Hausdorff topological vector spaces. Springer Science+Business Media, LLC, 2011 Commutative nationallicence Cancellative semigroup nationallicence Semigroup symmetry nationallicence Involutive group nationallicence Minkowski-Rådström-Hörmander space nationallicence Grzybowski J. Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland aut Pallaschke D. University of Karlsruhe, Kaiserstr. 12, 76128, Karlsruhe, Germany aut Przybycień H. Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland aut Urbański R. Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland aut Semigroup Forum Springer-Verlag 83/3(2011-12-01), 447-456 0037-1912 83:3<447 2011 83 233 https://doi.org/10.1007/s00233-011-9327-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9327-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grzybowski J. Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland aut NATIONALLICENCE 700 1- Pallaschke D. University of Karlsruhe, Kaiserstr. 12, 76128, Karlsruhe, Germany aut NATIONALLICENCE 700 1- Przybycień H. Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland aut NATIONALLICENCE 700 1- Urbański R. Adam Mickiewicz University, Umultowska 87, 61-614, Poznań, Poland aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/3(2011-12-01), 447-456 0037-1912 83:3<447 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer