2000 Fiscal Year Final Research Report Summary
Ring extensions and quotient rings
| Project/Area Number |
11640014
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | TOKYO GAKUGEI UNIVERSITY |
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Principal Investigator |
YOSHIMI Tokuhiro (北村 好) Tokyo Gakugei Univ., Faculty of Education, Professor, 教育学部, 教授 (00014811)
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| Co-Investigator(Kenkyū-buntansha) |
SEKIZAWA Masami TOKYO GAKUGEI UNIVERSITY, Faculty of Education Professor, 教育学部, 教授 (80014835)
MIYACHI Jun-ichi TOKYO GAKUGEI UNIVERSITY, Faculty of Education associate Professor, 教育学部, 助教授 (50209920)
MASAIKE Kanzo TOKYO GAKUGEI UNIVERSITY, Faculty of Education Professor, 教育学部, 教授 (40015798)
IKEDA Yoshito TOKYO GAKUGEI UNIVERSITY, Faculty of Education associate Professor, 教育学部, 助教授 (70014834)
TANAKA Yoshio TOKYO GAKUGEI UNIVERSITY, Faculty of Education Professor, 教育学部, 教授 (90014810)
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| Project Period (FY) |
1999 – 2000
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| Keywords | quashi Frobenius eytension / artinian ring / noetherian ring / maximal quotient ring / module / full linear ring |
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| Research Abstract |
It is shown that for a quasi-Frobenius extension A of a right non-singular ring B if A is a right self-injective ring, then so is B.An example of a Frobenius extension A/B such that A is a simple Artinian ring but B is not a self-injective ring is given. Let A be a quasi-Frobenius extension of B.It is shown that if B_B is U-Noetherian for a right B-module U, then A is V : =Hom_B(A, U)-Noetherian. it is also shown that if U_B is a right B-module which is faithful, injective and torsionless, then the quotient ring of A with respect to V_A is a quasi-Frobenius extension of the quotient ring of B with respect to U_B.
Let R be a right semi-hereditary ring with a maximal right quotient ring Q such that Q is a left flat epimorphism of R.If Q is a direct product of right full linear rings, then R is a direct product of rings whose maximal right quotient rings are full linear rings.
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