Ordered groups and rings

[Zelda22]

(Z3,+3,*3,<z3) __an ordered group __an ordered ring
(Z,+,*,>z) __an ordered group __an ordered ring

I think (Z3,+3,*3,<z3) is not an ordered group, so it isn't an ordered ring.


and (z,+,*,>z) is not an ordered group either.
Am I correct? Please explain. Thanks

 

[blamocur]

Am I the only one who does not understand these notations?

 

[topsquark]

(Z3,+3,*3,<z3) __an ordered group __an ordered ring

Are you trying to say that you have an ordered ring of integers a modulo 3 under + and *? I would write this, perhaps, as [imath]( \mathbb{Z},+,*,>)[/imath]. I don't know what you mean by "+3" and "*3" and "<z3."

The problem with this is do we have [imath]-1 < 2 \text{ mod(3)}[/imath]? Usually we consider the equivalence sets [imath]\overline{1}, \overline{2}, \overline{3}[/imath] to be the group elements to be ordered. Is that your intent?

You are calling it an "ordered group." If we are extending this to a ring I'm assuming that you mean the group operation is +?

-Dan

 

[Zelda22]

Are you trying to say that you have an ordered ring of integers a modulo 3 under + and *? I would write this, perhaps, as [imath]( \mathbb{Z},+,*,>)[/imath]. I don't know what you mean by "+3" and "*3" and "<z3."

The problem with this is do we have [imath]-1 < 2 \text{ mod(3)}[/imath]? Usually we consider the equivalence sets [imath]\overline{1}, \overline{2}, \overline{3}[/imath] to be the group elements to be ordered. Is that your intent?

You are calling it an "ordered group." If we are extending this to a ring I'm assuming that you mean the group operation is +?

-Dan

Yes. An ordered ring of integers mod 3 under + and * ,< z mod 3

 

[blamocur]

I think (Z3,+3,*3,<z3) is not an ordered group, so it isn't an ordered ring.


and (z,+,*,>z) is not an ordered group either.
Am I correct? Please explain. Thanks

Can you explain your answers ?

 

[Steven G]

Am I the only one who does not understand these notations?

No.