2019
Том 71
№ 11

All Issues

Bavula V. V.

Articles: 5
Article (Russian)

Classification of modules of dimension $n$ and multiplicity 1 over the Weyl algebra $A_n$

Bavula V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 579-587

Modules of the Gelfand - Kirillov dimension $n$ and the multiplicity 1 over the Weyl algebra $A_n$ are classified.

Article (Russian)

Extreme modules over the Weyl algebra $A_n$

Bavula V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 9. - pp. 1187-1197

Certain classes of simple modules over generalized Weyl algebras (extreme modules, polynomial modules, and modules with strong $D$-torsion) are classified. For these algebras, analogs of the Bernshtein and Stafford theorems are proved.

Article (Russian)

Description of bilateral ideals in a class of noncommutative rings. II

Bavula V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 3. - pp. 307–312

For generalized Weyl algebras containing the universal enveloping algebra $U_{sl} (2, К)$ of the Lie algebra $sl (2)$ over a field with characteristic zero, bilateral ideals are classified. We show that a product of ideals is commutative and any proper ideal can be uniquely decomposed into a product of primary ideals.

Article (Russian)

Description of bilateral ideals in a class of noncommutative rings. I

Bavula V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 209–220

For generalized Weil algebras of degree 1 with base Dedekind ring, bilateral ideals are classified. The (noncommutative) algebras, in which the product of ideals is permutable and any proper ideal is uniquely decomposed into the product of prime ideals, are described.

Article (Ukrainian)

Simple D[X, Y; ?,a]-modules

Bavula V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 12. - pp. 1628–1644