Bezout Rings of Stable Range 1.5 and the Decomposition of a Complete Linear Group into the Product of its Subgroups

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

“…If the ring R has stable range 1.5, then some properties of the Zelisko group G Φ are closely related to a factorizability of the general linear group over R (see [13,Theorem 3,p. 144] and [10,Chapter 2.6]).…”

Commutative Bezout domains of stable range 1.5

“…This notion was introduced by the second author [18] and studied in [16,19]. Commutative principal ideal domains, adequate rings (see [14, Prorositions 3.15 and 3.14] and [1, Proposition 4]), rings of 2 × 2 matrices over rings listed before (see [18, Theorem 5, p. 856]) has stable range 1.5.…”

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

“…Note that the commutative rings of stable range 1.5 coincide with rings of almost stable range 1 (see [1,8]). Finally, certain properties of the Zelisko group G Φ are closely related to a factorizability of the general linear group over the ring R of stable range 1.5 (see [13,Theorem 3,p. 144], [10,Chapter 2.7], [6, Theorem 1.2.2., p. 12], [5], and [9]).…”