On the dimension of modules and algebras. I

Samuel Eilenberg, Masatoshi Ikeda, and Tadasi Nakayama

Source: Nagoya Math. J. Volume 8 (1955), 49-57.

Related Works:

See also: Samuel Eilenberg, Tadasi Nakayama. On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings. Nagoya Mathematical Journal vol. 9, (1955), pp. 1-16.

Project Euclid: euclid.nmj/1118799677

See also: Maurice Auslander. On the dimension of modules and algebras. III. Global dimension. Nagoya Mathematical Journal vol. 9, (1955), pp. 67-77.

Project Euclid: euclid.nmj/1118799684

See also: Samuel Eilenberg, Hirosi Nagao, Tadasi Nakayama. On the dimension of modules and algebras. IV. Dimension of residue rings of hereditary rings. Nagoya Mathematical Journal vol. 10, (1956), pp. 87-95.

Project Euclid: euclid.nmj/1118799771

See also: Samuel Eilenberg, Tadasi Nakayama. On the dimension of modules and algebras. V. Dimension of residue rings. Nagoya Mathematical Journal vol. 11, (1957), pp. 9-12.

Project Euclid: euclid.nmj/1118799855

See also: Maurice Auslander. On the dimension of modules and algebras. VI. Comparison of global and algebra dimension. Nagoya Mathematical Journal vol. 11, (1957), pp. 61-65.

Project Euclid: euclid.nmj/1118799859

Primary Subjects: 09.1X

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Permanent link to this document: http://projecteuclid.org/euclid.nmj/1118799619
Mathematical Reviews number (MathSciNet): MR0069157
Zentralblatt MATH identifier: 0066.28801

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References

[1] G. Azumaya and T. Nakayama, On absolutely uni-serial algebras, Jap. J. Math. 19 (1948), 263-273.

Mathematical Reviews (MathSciNet): MR11:316b

Zentralblatt MATH: 0039.26304

[2] R. Brauer and C. Nesbitt, On the regular representations of algebras, Proc. Nat. Acad. Sci. U.S.A. 23 (1937), 236-240.

Mathematical Reviews (MathSciNet): MR1503429

Zentralblatt MATH: 0019.10201

[3] H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press (1954).

[4] S. Eilenberg, Algebras of cohomologically finite dimension, Comment. Math. Helv. (to appear).

Mathematical Reviews (MathSciNet): MR16:442c

Zentralblatt MATH: 0058.02801

[5] M. Ikeda, H. Nagao and T. Nakayama, Algebras with vanishing -cohomology groups, Nagoya Math. 7 (1954),-.

Mathematical Reviews (MathSciNet): MR16:214f

Zentralblatt MATH: 0058.02703

[6] H. Nagao and T. Nakayama, On the structure of (Afo)- and (fM)-modules, Math. Zeit. 59(1953), 164-170. ColumbiaUniversity Osaka University Nagoya University

Mathematical Reviews (MathSciNet): MR15:195a

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