Invariant factors of products over elementary divisor domains

Elementary Divisor Domains and Bézout Domains

It is well-known that an Elementary Divisor domain R is a Bézout domain, and it is a classical open question to determine whether the converse statement is false. In this article, we provide new chains of implications between R is an Elementary Divisor domain and R is Bézout defined by hyperplane conditions in the general linear group. Motivated by these new chains of implications, we construct...

Formalized linear algebra over Elementary Divisor Rings in Coq

This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support essential operations of linear algebra, the classification theorem of finitely presented modules over such rings and the uniqueness of the Smith normal form up to...

On the Divisor Products and Proper Divisor Products Sequences*

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n. In this paper, we study the properties of the sequences {PdCn)} and {qd(n)}, and prove that the Makowski &. Schinzel conjecture hold for the sequences {pd(n)} and {qd(n)}.

Some Remarks About Elementary Divisor Rings

Some Remarks on Elementary Divisor Rings II