Zur Theorie des nichtkommutativen Polynombereichs und Quotientenrings

Schwarz, Ludwig

doi:10.1007/bf01447834

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1969

2004

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Cited by 5 publications

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“…It is interesting to note that in a paper of 1931, dedicated to the ring theoretic properties of the Weyl algebra, D. Littlewood arrived at the Ore condition independently of Ore. The time must have been ripe for this work because it has been claimed in [30] that the condition was also known to the members of E. Noether's circle in Germany.…”

Section: Fractionsmentioning

confidence: 98%

The Quest for Quotient Rings (Of Noncommutative Noetherian Rings)

Coutinho¹,

McConnell²

2003

The American Mathematical Monthly

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Section: Fractionsmentioning

confidence: 98%

The Quest for Quotient Rings (Of Noncommutative Noetherian Rings)

Coutinho¹,

McConnell²

2003

The American Mathematical Monthly

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Quotient rings

Elizarov¹

1969

Algebr Logic

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The concept of a quotient ring (more precisely, of a quotient field) was first introduced by E. Steinitz in his paper, "The algebraic theory of fields." In the sixty years since then the concept of quotient rings has been repeatedly generalized, and quotient rings are utilized in the most diverse branches of algebra.The present survey,* covering about 200 published works devoted to quotient rings in some sense or other, consists of five sections. The first four of these present results pertaining to classical, generalized classical, nonclassical, and constructive quotient rings. The last section is devoted to modules of quotients. In addition to this, in each of the preceding sections we consider the connections between the properties of the quotient ring of ring ~ and the properties of certain ~-modules, as well as the modular properties of the quotient ring.In this survey we do not consider quotient rings of topological rings or semigroups of quotients, although the theory of the latter is not far removed from that of quotient rings. We barely touch on works on the embedding of rings in fields which are not quotient fields or works on quotient rings of commutative rings in which questions which are specific to the commutative case are studied.

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Quotient Rings of Noncommutative Rings in the First Half of the 20th Century

Coutinho

2004

Archive for History of Exact Sciences

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Zur Theorie des nichtkommutativen Polynombereichs und Quotientenrings

Cited by 5 publications

References 1 publication

The Quest for Quotient Rings (Of Noncommutative Noetherian Rings)

The Quest for Quotient Rings (Of Noncommutative Noetherian Rings)

Quotient rings

Quotient Rings of Noncommutative Rings in the First Half of the 20th Century

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