Rings with minimum condition by Emil Artin

Cover of: Rings with minimum condition | Emil Artin

Published by University of Michigan Press in Ann Arbor .

Written in English

Read online

Subjects:

  • Algebraic fields.,
  • Rings (Algebra)

Edition Notes

Book details

Statementby Emil Artin, Cecil J. Nesbitt [and] Robert M. Thrall.
SeriesUniversity of Michigan publications in mathematics,, no. 1
ContributionsNesbitt, Cecil James, 1912-, Thrall, Robert McDowell, 1914-
Classifications
LC ClassificationsQA3 .M5 no. 1
The Physical Object
Paginationx, 123 p.
Number of Pages123
ID Numbers
Open LibraryOL187179M
LC Control Numbera 45000035
OCLC/WorldCa523704

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Rings with Minimum Condition. Description. Dealing with algebraic ring theory, this book was written for mathematicians who are familiar with groups, rings, fields, and Rings with minimum condition book properties.

Concepts such as vector spaces, matrix representations, simple rings, and semisimple rings. Rings and vector spaces --Minimum condition --Matrix representations --Semisimple rings --Simple rings --Kronecker products of spaces and rings --Simple rings continued --Splitting fields and crossed products --nonsemisimple rings with minimum condition.

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ORNSTEIN1 In what follows, a ring will always mean an associative ring with unit element. Definition. A ring R is said to satisfy the restricted minimum condi-tion (or to be a RM ring, for short), if Rings with minimum condition book each ideal A 9^ (0) in R, the ring R/A is right artinian.

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It is important to make a careful assessment of your product before specifying its condition. For information about selecting a condition for your product, see Selecting Conditions. The aim of this note is to study the structure of a $\Gamma$-ring (not in the sense of Nobusawa) with minimum conditions.

By ring theoretical techniques, we obtain various properties on the semi-prime $\Gamma$-ring and generalize Nobusawa's result which corresponds to the Wedderburn-Artin Theorem in ring by: 5.

The definition of Artinian rings may be restated by interchanging the descending chain condition with an equivalent notion: the minimum condition. A ring is left Artinian if it satisfies the descending chain condition on left ideals, right Artinian if it satisfies the descending chain condition on right ideals, and Artinian or two-sided Artinian if it is both left and right Artinian.

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