Noetherian semi-perfect rings of distributive module type

Author
Yu. Yaremenko
Kyiv University
Abstract
We prove that any noetherian semi-perfect ring of distributive module type is biserial.
Keywords
noetherian ring, semiperfect ring, distributive module type
DOI
doi:10.30970/ms.8.1.3-10
Reference
1. Camillo V. Distributive modules// J. Algebra V.36 –1975 p.16–25

2. Bass H Finitistic dimension and a homological generalisation of semiprimary rings // Trans. Amer. Math. Soc. V.95–1960 p.466–488

3. Muller B.J. On semi-perfect rings// Illinois J. Math. V.14 N.3–1970 p.464–467

4. Kasch F. Moduln und Ringe, B.G. Teubner,addr Stutgart–1977

5. Kirichenko V.V. Rings and modules, Kiev State University –1981

6. Kirichenko V.V. Generalized uniserial rings// Mat. sbornik V.99–1976 N.4 p.559–581

7. Tuganbaev A.A. Semi-distributive rings// Abstract of reports of XIX All Union Algebraic Conf., part 1, Lviv–1987

8. Kirichenko V.V., Khibina M.A. Semi-perfect semi-distributive ringsInfinite groups and related algebraic topics ,addr Kiev, Math. Institute–1993 p.457–480

9. Kirichenko V.V., Kostukievich P.P., Yaremenko Yu.V. Biserial rings and modules over themAlgebraic structures and its application ,addr Kiev, SMK HE–1988

10. Fuller K.R. Weakly symmetric rings of distributive module type// Comm. in Algebra–1977 N.5 p.997–1008

11. Kirichenko V.V., Kostukievich P.P. Biserial rings// Ukr. Mat. J. V.38–1986 N.6 p.718–723

12. Colby R.R., Fuller K.R. Modules over biserial rings// Comn. in Algebra–1981 N.9 p.511–532

13. Danlyev H.M., Kirichenko V.V., Haleckaya Z.P., Yaremenko Yu.V., Weakly prime semi-perfect 2-rings and modules over them Algebraic researches, Institute of Mathematics NAS Ukraine–1995 p. 5–32

14. Gabriel P. Unzerlegbare Darstellungen I// Manuscript Math.–1972 V.6 p.71–103

15. Krugliak S.A. Representations of algebras which square of radical is zero// Zap. Nauk. Sem. LOMI, USSR V.28 –1972 p.80–89

16. Drozd Yu.A. Minors and reduction theorems// Coll. Math. Soc. J. Bolyai–1971 N.6 p.173–176

17. Morita K. Duality for modules and its applications to the theory of rings with minimum condition// Sc. Rep. Tokyo Kyoiku Daigaku V.6 –1958 p.83–142

18. Kirichenko V.V. Decomposition theorems for semi-perfect rings in Mat. Studii

19. Kirichenko V.V., Yaremenko Yu.V. Multiserial rings// Ukr. Math. J. V.48–1996 N.9 p.1223–1336

20. Michler C Structure of semi-perfect hereditary noetherian rings // J. Algebra V.13–1969 p.327–344

21. Kirichenko V.V., Mogileva V.V., Pirus E.M., Khibina M.A. Semi-perfect rings and piecewise domainsAlgebraic researches , Institute of Mathematics NAS Ukraine–1995 p.33–65

Pages
3-10
Volume
8
Issue
1
Year
1997
Journal
Matematychni Studii
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