Semi-perfect rings in which every
ideal is idempotent

L.~Mashchenko

We prove that the quiver of a right noetherian semi-perfect indecomposable ring in which every nonradical ideal is idempotent contains at most two vertices. If such a ring is semi-distributive, it is serial and two-sided notherian. Conversely, if the quiver of a serial indecomposable two-sided notherian ring contains at most two vertices then every nonradical ideal of this ring is idempotent.

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	Semi-perfect rings in which every ideal is idempotent
Author	L.~Mashchenko Kyiv University
Abstract	We prove that the quiver of a right noetherian semi-perfect indecomposable ring in which every nonradical ideal is idempotent contains at most two vertices. If such a ring is semi-distributive, it is serial and two-sided notherian. Conversely, if the quiver of a serial indecomposable two-sided notherian ring contains at most two vertices then every nonradical ideal of this ring is idempotent.
Keywords	quiver, right noetherian ring, semiperfect indecomposable ring, nonradical idempotent ideal, semi-distributive ring, serial ring
DOI	doi:10.30970/ms.7.2.129-132
Reference	1. Faith C. Algebra II, Ring Theory. — Springer-Verlag, Berlin–Heidelberg–New-York, 1976. 2. Algebraic researches. — Institute of Mathematics NAS Ukraine, 1995. 3. Michler G. Idempotent ideals in perfect rings // Canad. J. Math. 1969, V.21, ¹2, P.301–309. 4. Clifford A.N., Preston G.B. The algebraic theory of semi-groups. — AMS, 1964, V.1. 5. Kasch F. Moduln und Ringe. — B.G.Teubner, Stuttgart, 1977. 6. Muller B.J. On semi-perfect rings // Illinois J. Math. , 1970, V.14, ¹3, P.464–467. 7. Kirichenko V.V., Khibina M.A. Semi-perfect semi-distributive rings. Infinite groups and related algebraic topics // Kiev, Math. Institute, 1993, P.457–480. 8. Kirichenko V.V. Rings and modules. — Kiev St. Univ. 1981. 9. Kirichenko V.V., Generalized uniserial rings // Mat. sbornik, 1976, V.99, ¹4, P.559–581.
Pages	129-132
Volume	7
Issue	2
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Semi-perfect rings in which every ideal is idempotent