maximal and classical rings of quotients

1971 ◽  
pp. 110-129
Author(s):  
Bo Stenström
Keyword(s):  
Rings Of Quotients

RATIONALLY ℵα-COMPLETE COMMUTATIVE RINGS OF QUOTIENTS

2009 ◽  
Vol 08 (05) ◽  
pp. 601-615
Author(s):  
JOHN D. LAGRANGE
Keyword(s):  
Commutative Rings ◽  
Von Neumann ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Ring Of Quotients ◽  
Rings Of Quotients ◽  
Special Case ◽  
Regular Rings

If {Ri}i ∈ I is a family of rings, then it is well-known that Q(Ri) = Q(Q(Ri)) and Q(∏i∈I Ri) = ∏i∈I Q(Ri), where Q(R) denotes the maximal ring of quotients of R. This paper contains an investigation of how these results generalize to the rings of quotients Qα(R) defined by ideals generated by dense subsets of cardinality less than ℵα. The special case of von Neumann regular rings is studied. Furthermore, a generalization of a theorem regarding orthogonal completions is established. Illustrative example are presented.

Clifford semigroups of left quotients

1986 ◽  
Vol 28 (2) ◽  
pp. 181-191 ◽  
Author(s):  
Victoria Gould
Keyword(s):  
Ring Theory ◽  
Clifford Semigroups ◽  
Ring Of Quotients ◽  
Rings Of Quotients ◽  
Classical Ring ◽  
Number Of Authors

Several definitions of a semigroup of quotients have been proposed and studied by a number of authors. For a survey, the reader may consult Weinert's paper [8]. The motivation for many of these concepts comes from ring theory and the various notions of rings of quotients. We are concerned in this paper with an analogue of the classical ring of quotients, introduced by Fountain and Petrich in [3].

Rings of Quotients

2017 ◽  
pp. 247-251
Author(s):  
Jonathan S. Golan ◽  
Tom Head
Keyword(s):  
Rings Of Quotients

Classical rings of quotients of semiprimePI-rings

1993 ◽  
Vol 32 (1) ◽  
pp. 1-8 ◽  
Author(s):  
K. I. Beidar
Keyword(s):  
Rings Of Quotients

Continuous and pf rings of quotients

1988 ◽  
pp. 94-105
Author(s):  
J. L. García Hernández
Keyword(s):  
Rings Of Quotients

scholarly journals Near-rings of quotients of endomorphism near-rings

1975 ◽  
Vol 19 (4) ◽  
pp. 345-352 ◽  
Author(s):  
Michael Holcombe
Keyword(s):  
Additive Group ◽  
Finite Products ◽  
Definition Of ◽  
Group Object ◽  
Rings Of Quotients ◽  
Natural Way

Let be a category with finite products and a final object and let X be any group object in . The set of -morphisms, (X, X) is, in a natural way, a near-ring which we call the endomorphism near-ring of X in Such nearrings have previously been studied in the case where is the category of pointed sets and mappings, (6). Generally speaking, if Γ is an additive group and S is a semigroup of endomorphisms of Γ then a near-ring can be generated naturally by taking all zero preserving mappings of Γ into itself which commute with S (see 1). This type of near-ring is again an endomorphism near-ring, only the category is the category of S-acts and S-morphisms (see (4) for definition of S-act, etc.).

Rings of Quotients of Group Rings

1969 ◽  
Vol 21 ◽  
pp. 865-875 ◽  
Author(s):  
W. D. Burgess
Keyword(s):  
Group Ring ◽  
Group Rings ◽  
Maximum Condition ◽  
Regular Group ◽  
Von Neumann ◽  
Von Neumann Regular ◽  
Completely Reducible ◽  
Rings Of Quotients ◽  
Prime Case

The group ring AG of a group G and a ring A is the ring of all formal sums Σg∈G agg with ag ∈ A and with only finitely many non-zero ag. Elements of A are assumed to commute with the elements of G. In (2), Connell characterized or completed the characterization of Artinian, completely reducible and (von Neumann) regular group rings ((2) also contains many other basic results). In (3, Appendix 3) Connell used a theorem of Passman (6) to characterize semi-prime group rings. Following in the spirit of these investigations, this paper deals with the complete ring of (right) quotients Q(AG) of the group ring AG. It is hoped that the methods used and the results given may be useful in characterizing group rings with maximum condition on right annihilators and complements, at least in the semi-prime case.

Topological Rings of Quotients

1974 ◽  
Vol 26 (5) ◽  
pp. 1228-1233 ◽  
Author(s):  
William Schelter
Keyword(s):  
Compact Space ◽  
Topological Ring ◽  
Ring Of Quotients ◽  
Algebraic Ring ◽  
Rings Of Quotients

We investigate here the notion of a topological ring of quotients of a topological ring with respect to an arbitrary Gabriel (idempotent) filter of right ideals. We describe the topological ring of quotients first as a subring of the algebraic ring of quotients, and then show it is a topological bicommutator of a topological injective R-module. Unlike R. L. Johnson in [6] and F. Eckstein in [2] we do not always make the ring an open subring of its ring of quotients. This would exclude examples such as C(X), the ring of continuous real-valued functions on a compact space, and its ring of quotients as described in Fine, Gillman and Lambek [3].

Functional Identities and Rings of Quotients

2016 ◽  
Vol 19 (6) ◽  
pp. 1437-1450
Author(s):  
Matej Brešar
Keyword(s):  
Functional Identities ◽  
Rings Of Quotients
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