Physical Sciences and Mathematics Commons^™

Study On Algebras With Retractions And Planes Over A Dvr., Prosenjit Das Dr.

Doctoral Theses

Aim:The main aim of this thesis is to study the following problems:1. For a Noetherian ring R, to find a set of minimal sufficient fibre conditions for an R-algebra with a retraction to R to be an A1-fibration over R.2. To investigate sufficient conditions for a factorial A1-form, with a retraction to the base ring, to be A1.3. To investigate whether planes of the form b(X, Y)Zn – a(X, Y) are co- ordinate planes in the polynomial ring in three variables X, Y and Z over a discrete valuation ring.The 1st problem will be discussed in Chapter 3 entitled Codimension- …