Decomposition theorems for
semi-perfect rings

V. Kirichenko

We propose a general method for constructing two-sided Pierce decomposition of a semi-perfect ring using the structure of its quivers. As a sequence, we obtain the decomposition theorems for various classes of semi-perfect rings.

1. H. Bass, Finitistic dimension and homological generalization of semi-primary rings // Trans. AMS V.95 --1960, p.466--488

2. C. Faith Algebra II Ring Theory, Springer-Verlag ,addr Berlin-Heidelberg-New York –1976

3. F. Kasch Moduln und Ringl, B.G.Teubner,addr Stuttgart-1977

4. V.V. Kirichenko Rings and modules, Kiev State University-1981

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

6. V.V. Kirichenko Semi-perfect rings and their quivers// Ann.St.Univ.Ovidius, Constanza V.–1996 N.2

7. F.R. Gantmaher Theory of matrices, Nauka,addr Moscow –1967

8. P. Lankaster Theory of matrices, Academic Press,addr New York-London–1969

9. V.A. Emelichev, O.B. Melnikov, V.I. Sarvanov, R.I. Tyshkevich Lectures in graph theory,addr Moscow, Nauka– 1990

10. Richard S. Pierce Associative Algebras, Springer-Verlag,addr New York-Heidelberg-Berlin– 1982

11. J. Lambek Lectures on Rings and Modules, Blaisdell-Ginn ,addr Waltham-Toronto-London–1966

12. V.V. Kirichenko, Samir Valio, Yu.V. Yaremenko Semi-perfect rings and their quivers Infinite groups and related algebraic topics,addr Kiev, Math. Institute– 1993 p.438–456

13. V.V. Kirichenko Hereditary and semi-hereditary serial ring// Zap. Nauch. sem. LOMI V.114–198 p.137–147

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

	Decomposition theorems for semi-perfect rings
Author	V. Kirichenko Kiev University
Abstract	We propose a general method for constructing two-sided Pierce decomposition of a semi-perfect ring using the structure of its quivers. As a sequence, we obtain the decomposition theorems for various classes of semi-perfect rings.
Keywords	two-sided Pierce decomposition, semi-perfect ring, quiver structure, decomposition theorems
DOI	doi:10.30970/ms.8.2.157-161
Reference	1. H. Bass, Finitistic dimension and homological generalization of semi-primary rings // Trans. AMS V.95 --1960, p.466--488 2. C. Faith Algebra II Ring Theory, Springer-Verlag ,addr Berlin-Heidelberg-New York –1976 3. F. Kasch Moduln und Ringl, B.G.Teubner,addr Stuttgart-1977 4. V.V. Kirichenko Rings and modules, Kiev State University-1981 5. V.V Kirichenko Generalized uniserial rings// Mat. sb. V.99 N.4– 1976 p.559–581 6. V.V. Kirichenko Semi-perfect rings and their quivers// Ann.St.Univ.Ovidius, Constanza V.–1996 N.2 7. F.R. Gantmaher Theory of matrices, Nauka,addr Moscow –1967 8. P. Lankaster Theory of matrices, Academic Press,addr New York-London–1969 9. V.A. Emelichev, O.B. Melnikov, V.I. Sarvanov, R.I. Tyshkevich Lectures in graph theory,addr Moscow, Nauka– 1990 10. Richard S. Pierce Associative Algebras, Springer-Verlag,addr New York-Heidelberg-Berlin– 1982 11. J. Lambek Lectures on Rings and Modules, Blaisdell-Ginn ,addr Waltham-Toronto-London–1966 12. V.V. Kirichenko, Samir Valio, Yu.V. Yaremenko Semi-perfect rings and their quivers Infinite groups and related algebraic topics,addr Kiev, Math. Institute– 1993 p.438–456 13. V.V. Kirichenko Hereditary and semi-hereditary serial ring// Zap. Nauch. sem. LOMI V.114–198 p.137–147 14. V.V. Kirichenko, M.A. Khibbina Semi-perfect semi-distributive ringsInfinite groups and related algebraic topics,addr Kiev , Math Institute–1993 p.457–480
Pages	157-161
Volume	8
Issue	2
Year	1997
Journal	Matematychni Studii
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Table of content of issue	html

Decomposition theorems for semi-perfect rings