Commutative Bezout domains of stable range 1.5

Generating solutions of a linear equation and structure of elements of the Zelisko group

“…This notion arose as a modification of the Bass's concept of the stable range of rings (see [2, p. 498]). The examples of rings of stable range 1.5 are Euclidean rings, principal ideal rings, rings of algebraic integers, rings of integer analytic functions, adequate rings [10, p. 20] and [3]. Note that the commutative rings of stable range 1.5 coincide with rings of almost stable range 1 [1,8].…”

Generating solutions of a linear equation and structure of elements of the Zelisko group II

“…This notion arose as a modification of the Bass's concept of the stable range of rings (see [2, p. 498]). Examples of rings of stable range 1.5 are Euclidean rings, principal ideal rings, factorial rings, rings of algebraic integers, rings of integer analytic functions, and adequate rings (see [3,4] and [10, p. 21]). Note that the commutative rings of stable range 1.5 coincide with rings of almost stable range 1 (see [1,8]).…”

A greatest common divisor and a least common multiple of solutions of a linear matrix equation

“…Note that a commutative elementary divisor domain is a commutative domain over which each matrix is equivalent to a diagonal matrix, each diagonal element (invariant factor) divides the next one. Examples of elementary divisor rings are Euclidean rings, principal ideal rings, adequate rings, a ring of formal power series over a field of rational numbers with a free integer term (see [9,10]).…”