√Morita theory Formal ring laws and monoidal equivalences of categories of bimodules

Mitsuhiro TAKEUCHI

doi:10.2969/jmsj/03920301

√Morita theory

Formal ring laws and monoidal equivalences of categories of bimodules

Mitsuhiro TAKEUCHI

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 2 Pages 301-336

DOI https://doi.org/10.2969/jmsj/03920301

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Published: 1987 Received: October 16, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : √<Morita> theory-Formal ring laws and monoidal equivalences of categories of bimodules-
Right : √Morita theory

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : To the memory of Professor Akira Hattori
Right : Formal ring laws and monoidal equivalences of categories of bimodules

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Eilenberg and G. M. Kelly, Closed categories, Proc. Conf. Categorical Algebra, La Jolla 1965, Springer-Verlag, 1966, pp. 421-562.
2) B. Pareigis, Morita equivalence of module categories with tensor products, Comm. Algebra, 9 (1981), 1455-1477.
3) D. Riffelmacher, Multiplication alteration and related rigidity properties of algebras, Pacific J. Math., 71 (1977), 139-157.
4)=[MA) M. Sweedler, Multiplication alteration by two-cocycles, Illinois J. Math., 15 (1971), 302-323.
5) [MA) M. Sweedler, Groups of simple algebras, Publ. Math. I.H.E.S., 44 (1975), 79-189.
6)=[GA) M. Takeuchi, Groups of algebras over A⊗A, J. Math. Soc. Japan, 29 (1977), 459-492.
7)=[GA) M. Takeuchi, Ext_ad(Sp R, μ^A)_??_Br(A/k), J. Algebra, 67 (1980), 436-475.
8)=[GA) M. Takeuchi, Introduction to √<Morita> theory, Proc. 17th Symp. Ring Theory, 1984, pp. 78-86.
9)=[GA) M. Takeuchi, Equivalences of categories of algebras, Comm. Algebra, 13 (1985), 1931-1976.

Right : [1] S. Eilenberg and G. M. Kelly, Closed categories, Proc. Conf. Categorical Algebra, La Jolla 1965, Springer-Verlag, 1966, pp. 421-562.
[2] B. Pareigis, Morita equivalence of module categories with tensor products, Comm. Algebra, 9 (1981), 1455-1477.
[3] D. Riffelmacher, Multiplication alteration and related rigidity properties of algebras, Pacific J. Math., 71 (1977), 139-157.
[4]=[MA] M. Sweedler, Multiplication alteration by two-cocycles, Illinois J. Math., 15 (1971), 302-323.
[5] [MA] M. Sweedler, Groups of simple algebras, Publ. Math. I. H. E. S., 44 (1975), 79-189.
[6]=[GA] M. Takeuchi, Groups of algebras over A⊗A, J. Math. Soc. Japan, 29 (1977), 459-492.
[7]=[GA] M. Takeuchi, Ext_ad(Sp R, μ^A)≅Br(A/k), J. Algebra, 67 (1980), 436-475.
[8]=[GA] M. Takeuchi, Introduction to √Morita theory, Proc. 17th Symp. Ring Theory, 1984, pp. 78-86.
[9]=[GA] M. Takeuchi, Equivalences of categories of algebras, Comm. Algebra, 13 (1985), 1931-1976.

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