Register to reply

Semi-groups and monoids

by quasar987
Tags: monoids, semigroups
Share this thread:
Feb12-07, 07:07 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,771
My topology teacher appears to call a monoid a set with an associative binary operation, but with no identity element. According to wiki, this is the definition of a semi-group, although they remark that some authors define semi-groups as having an identity (i.e. synonymously to monoid). But they don't say on the monoid article that some authors take monoid to mean an associative magma(groupoid) with no identity.

So, does my teacher simply has the definitions mixed up or do some authors effectively call 'monoid' an associative magma(groupoid)?

I wanted to ask here before throwing the "Sir professor, according to wikipedia, you're wrong" at him. I'm sure that's understandable.
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
Feb13-07, 12:26 AM
P: 11
IMOH, arguments over terminology are politically dangerous, only attempt this if you are on good terms with your professor, or want to start a fight.

In my experience, semi-group means associative binary operation, and monoid means associative binary operation with identity element. Wolfram's mathworld agrees:, I usually trust Wolfram for ORTHODOX definitions, wikipedia is good at bringing in side issues and lesser known usage (ok, that's my subjective opinion).
Feb13-07, 12:33 AM
Sci Advisor
HW Helper
P: 2,020
Yeah, I wouldn't recommend telling him he's "wrong", but you might want to tell him that you've seen it mean something else in (many) other standard references. Like, for example, in Rotman's Theory of Groups.

matt grime
Feb13-07, 03:37 AM
Sci Advisor
HW Helper
P: 9,396
Semi-groups and monoids

You could tell him. Though he's likely to be unimpressed that you used Wiki as a source, and even less impressed that you're worrying about this than actually learning the course.

It's just a name, and mostly unimportant. It is the definition that is important. Ok, it might cause you some confusion when looking in other textbooks.
Feb13-07, 05:59 AM
P: 406
Quote Quote by ecurbian View Post
IMOH, arguments over terminology are politically dangerous, only attempt this if you are on good terms with your professor, or want to start a fight.
Quite a lot of even modern mathematical definitions are not standardised with subtle and not so subtle differences cropping up all over the place. Many books will even use different "derivation trees" if you will to arrive at some concepts and objects earlier or later than others would.

Register to reply

Related Discussions
More algebra...MONOIDS, etc Calculus & Beyond Homework 10
Couple questions involving monoids/isomorphisms Calculus & Beyond Homework 8
Centers of groups and products of groups Calculus & Beyond Homework 1
Wallpaper Groups, Free Groups, and Trees Introductory Physics Homework 13
References on monoids and applications? General Math 0