On the divided power structures in super-rings.

摘要

Given a super-commutative ring A=A0 direct summed with A1, does (A0,A1A1) always have a divided power structure? We give an example proving the answer is no. There exists a super-commutative ring SR=SR0 direct summed with SR1 with no divided power structure possible on (SR0,SR 1SR1). Also, we study super divided power structures and the properties they force onto divided power structures on the even part of a ring-ideal pair. We show that there can exist a divided power structure on the even part that is incompatible with the super divided power structure.;Also, just for fun, we explore the phenomenon of upper-Sierpinski-triangular matrices and where they manifest.