#### Semester ended

Congratulations to all members on a successful end of the Spring, 2019 semester. New registration is on September; we are looking forward to seeing you soon.

Congratulations to all members on a successful end of the Spring, 2019 semester. New registration is on September; we are looking forward to seeing you soon.

#### Bezout rings stable range and its generalizations

Let R be a Bezout domain of stable range one satisfying Dubrovin and Z conditions. Let R be a Bezout domain of stable range one satisfying Dubrovin and Z conditions. Then R is an elementary divisor ring. Then R is an elementary divisor ring. Let R be a commutative Bezout domain. Then a is a semipotent element if and only if R/aR is a semipotent ring. Let R be a Bezout duo-domain of Gelfand range one. Then R is an…

#### Presentation of the book «Factorization of matrices over elementary divisor ring…

The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a close relationship between the matrix factorization and specific properties of ubgroups of the complete linear group and the special normal form of matrices with respect to unilateral equivalence. The properties of matrices over rings of stable range 1.5 are thoroughly studied.

#### Type conditions of stable range to identify a new classes of rings that qualitat…

Introduced a new concept of stable range, which allowing introduce a new classes of rings which generalize of regular (von Neumann) rings, a local regular rings, semi-hereditary rings and almost clean rings

#### Reduction matrices over Bezout rings

Theorem 1. A Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. Theorem 2. Let R be a semiexchange quasi-duo Bezout ring. Then R is a ring with elementary reduction of matrices if and only if it is a duo. Theorem 3. Let R be a commutative e-atomic ring. The following statements are equivalent: (1) R - ring with elementary reduction of matrices; (2) R - Bezout ring. Theorem 4. Let R be a…

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Department of Algebra and Logic

Faculty of Mechanics and Mathematics

Ivan Franko National University of L'viv

1 Universytetska Str., 79000 Lviv, Ukraine

Tel: (+380 322) 394 172

E-mail: oromaniv at franko.lviv.ua