* groupoids and categories
@ 2015-03-09 15:51 Ronnie Brown
0 siblings, 0 replies; only message in thread
From: Ronnie Brown @ 2015-03-09 15:51 UTC (permalink / raw)
To: categories
Just to make a correction: I wrote "Brandy in 1926" instead of "Brandt
in 1926"!
To say more on this story, my survey article of 1987 writes:
-------------------------------------
Brandt???s de???nition of groupoid arose out of his work for over thirteen
years [6-10] on generalising to quaternary quadratic forms a composition
of binary quadratic forms due to Gauss [63]. Brandt then saw how to use
the notion of groupoid in generalising to the non-commutative case the
arithmetic of ideals in rings of algebraic integers, replacing the
classical ???nite abelian group by a ???nite groupoid [12].
--------------------------------------
[12] is H. BRANDT, ???Idealtheorie in Quaternionenalgebren???, Math. Ann.
99 (1928) 1-29.
A review by Baer of Jacobson's 1943 book on "The theory of rings" writes:
It is shown that for the two-sided ideals in an order one may
obtain unique factorization in the classical sense, including the
commutativity of multiplication, and that under comparatively
simple necessary conditions on the orders in the ring one
may construct Brandt's groupoid of ideals.
------------------------
The 1939 Monograph by A A Albert, who was at Chicago, may also say
something but I do not have it to hand. Use of groupoids in this area
was surely common knowledge in the 1940s. I also came across published
correspondence of Hasse on this topic.
Ronnie Brown
--
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2015-03-09 15:51 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2015-03-09 15:51 groupoids and categories Ronnie Brown
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).