Hi(Hi)

What happen if i drop the identity rule in the definition of a group?

What happen if a mathematical system does not have identity rule?

Are there any mathematical system that doesn't have identity rule?

(Wondering)

Printable View

- October 25th 2012, 03:07 PMerich22A mathematics system without identity rule?
Hi(Hi)

What happen if i drop the identity rule in the definition of a group?

What happen if a mathematical system does not have identity rule?

Are there any mathematical system that doesn't have identity rule?

(Wondering) - October 25th 2012, 03:21 PMjohnsomeoneRe: A mathematics system without identity rule?
That's too vague to say anything of substance to in reply.

However, in general, the identity represents the "change nothing" operation/element/whatever, and so is almost always found in math structures.

The one place I can recall where the identity was notably missing was in Ring Theory, where the *multiplicative* identity was sometimes excluded. I saw them called "rngs" rather than "rings" (get it? no "i" - hahaha, those witty mathematicians), but it's common to hear "ring with identity" to remove any uncertainty. However, even for rngs, there was always the identity of the additive operation (rng, + , 0). - October 25th 2012, 03:45 PMPlatoRe: A mathematics system without identity rule?
I absolutely agree with the statement:

**"That's too vague to say anything of substance to in reply."**

Here are comments.

The concept ofis associated with*identity***an operation.**

There are operations without identities.

Do you mean to say that all mathematical system must have operation(s)? - October 25th 2012, 04:08 PMerich22Re: A mathematics system without identity rule?
Thank you very much, john(Bow).

I've just read the requirement of a vector space, i just wonder if the identity rule is really needed? what about the requirement in a group, i just wonder, thanks for the answer. Hmmmm, so there is a system like rngs ((Giggle)) that doesn't have identity rule(Talking).

Ok, thank you so much, i want to investigate the rngs(Cool). - October 25th 2012, 04:14 PMerich22Re: A mathematics system without identity rule?
Thank you so much Plato(Bow).

Ok, I get it, so identity must be associated with an operation(Thinking).

Could you tell me any mathematical system that doesn't have identity rule except the rngs mentioned by john(Wink). I want to study this topic a little further through the examples.

Your post makes me wondering, are there any mathematical system that doesn't have any operation(Evilgrin)? - October 25th 2012, 07:51 PMemakarovRe: A mathematics system without identity rule?
A semigroup is a group without identity or inverse, i.e. only with associativity.

- October 25th 2012, 11:31 PMerich22Re: A mathematics system without identity rule?
Thanks emakarov, so what i need to see is semigroup. Ok:).