Date of Award

2014

Degree Type

Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Shapiro, Ilya

Keywords

Pure sciences, Crystalline cohomology, Divided powers, Sierpinski's triangle, Super-rings, Upper-sierpinski-triangular matrices

Rights

CC BY-NC-ND 4.0

Abstract

Given a super-commutative ring A=A 0 direct summed with A 1 , does (A 0 ,A 1 A 1 ) always have a divided power structure? We give an example proving the answer is no. There exists a super-commutative ring SR=SR 0 direct summed with SR 1 with no divided power structure possible on (SR 0 ,SR 1 SR 1 ). 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.

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