Let R be a ring with an endomorphismσ,F∪{0}the free monoid generated by U={u1,…,ut}with 0 added,and M a factor of F obtained by setting certain monomials in F to 0 such that M^(n)=0 for some n.Then we can form the ...Let R be a ring with an endomorphismσ,F∪{0}the free monoid generated by U={u1,…,ut}with 0 added,and M a factor of F obtained by setting certain monomials in F to 0 such that M^(n)=0 for some n.Then we can form the non-semiprime skew monoid ring R[M;σ].A local ring R is called bleached if for any j∈J(R)and any u∈U(R),the abelian group endomorphisms l_(u)−r_(j) and l_(j)−r_(u) of R are surjective.Using R[M;σ],we provide various classes of both bleached and non-bleached local rings.One of the main problems concerning strongly clean rings is to characterize the rings R for which the matrix ring M_(n)(R)is strongly clean.We investigate the strong cleanness of the full matrix rings over the skew monoid ring R[M;σ].展开更多
文摘Let R be a ring with an endomorphismσ,F∪{0}the free monoid generated by U={u1,…,ut}with 0 added,and M a factor of F obtained by setting certain monomials in F to 0 such that M^(n)=0 for some n.Then we can form the non-semiprime skew monoid ring R[M;σ].A local ring R is called bleached if for any j∈J(R)and any u∈U(R),the abelian group endomorphisms l_(u)−r_(j) and l_(j)−r_(u) of R are surjective.Using R[M;σ],we provide various classes of both bleached and non-bleached local rings.One of the main problems concerning strongly clean rings is to characterize the rings R for which the matrix ring M_(n)(R)is strongly clean.We investigate the strong cleanness of the full matrix rings over the skew monoid ring R[M;σ].
