Divisibility and Factorization of Kernel Functors

Abstract

In this article we explore the semigroup of kernel functors associated to a generalized discrete valuation ring. We will show that, among other interesting features, this semigroup is linearly ordered under divisibility, and we will present a factorization of kernel functors in terms of irreducible elements. The asymmetry of the divisibility condition will also be considered. In a way, these results are closely related to (and in the spirit of) the corresponding results obtained by Brungs for the lattice of ideals of this type of rings.

Keywords:

2000 AMS Subject Classification:

• 13C12
• 16L30
• 06F05
• 13D30

Acknowledgments

Notes

^#Communicated by R. Wisbauer.