78,501 research outputs found
Commutators and Anti-Commutators of Idempotents in Rings
We show that a ring has two idempotents with an invertible
commutator if and only if for a
ring in which is a sum of two units. In this case, the
"anti-commutator" is automatically invertible, so we study also
the broader class of rings having such an invertible anti-commutator. Simple
artinian rings (along with other related classes of matrix rings) with
one of the above properties are completely determined. In this study, we also
arrive at various new criteria for {\it general\} matrix rings.
For instance, is such a matrix ring if and only if it has an invertible
commutator where .Comment: 21 page
HOMFLY-PT skein module of singular links in the three-sphere
For a ring , we denote by the free -module spanned by
the isotopy classes of singular links in . Given two invertible
elements , the HOMFLY-PT skein module of singular links in (relative to the triple ) is the quotient of by
local relations, called skein relations, that involve and . We compute
the HOMFLY-PT skein module of singular links for any such that
and are invertible. In particular, we deduce the
Conway skein module of singular links
- …