• A FLAVOUR OF NON COMMUTATIVE ADVANCE ALGEBRA PART - II

Abstract

In this paper, A Flavour of Non Commutative Advance Algebra Part-I as we mentioned earlier unlike the case for Nagendram commutative near-field spaces, a non commutative near-field space N used not have a near-field of fractions in which all non zero divisors are invertible. But we claimed that there are alternatives, and we saw that one of these is the maximal Nagendram near-field space of left quotients. Here we shall see that there are other viable choices, all sub near-field spaces of the maximal Nagendram near-field space. It also turns out that these various Nagendram near-field spaces of quotients are characterized by topologies on Nagendram near-field space N and by “torsion” functors on N- sub Nagendram near-field spaces. Here we will give a brief introduction to topologies and torsion theories for N and give some indication of how they are connected. As a bonus we also characterize Nagendram commutative near-field spaces, a non commutative near-field space N of left quotients. Those characterizations are due to Dr N V Nagendram who published them in a series of papers in the academic year of 2019 -2020. This is the final part of a short two-part write-up on non commutative advanced algebra.