A generating solution of a linear equation and structure of elements of the Zelisko group

Volodymyr Shchedryk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

Victor Bovdi

United Arab Emirates University,
Al Ain, UAE

February 23, 2021 at 15:00 online

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Abstract of talk

Solutions of a linear equation $a= bx$ in a homomorphic image of a commutative Bezout domain of stable range 1.5 is developed.
It is proved that the set of solutions of a solvable linear equation contains at least one solution that divides the rest, which is
called a generating solution. Generating solutions are pairwise associates. Using this result, the structure of elements of the
Zelisko group is investigated.