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Study On Algebras With Retractions And Planes Over A Dvr., Prosenjit Das Dr.
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- …
Sequences Of Positive Integers Containing No K-Term Arithmetic Progressions And Smooth Numbers In Short Intervals., Goutam Pal Dr.
Sequences Of Positive Integers Containing No K-Term Arithmetic Progressions And Smooth Numbers In Short Intervals., Goutam Pal Dr.
Doctoral Theses
In my thesis I have worked on two problems:1. On sequences of positive integers containing no k terms in arithmetic progressions.2. On smooth numbers in short intervals.The first two chapters of my thesis deal with the first problem and in the rest of the thesis I have focused on the 2nd problem.In the first chapter of my thesis I have considered the function rk(N) for a fixed k ≥ 3, where, by definition, rk(N) is the cardinality of a maximal subset of N consecutive natural numbers with the property that nork terms of it are in an Arithmetic Progression (A. …