I Zero Element in a Ring: The 0 Ring Has Only One Element

chwala
Gold Member
Messages
2,827
Reaction score
415
TL;DR
Am just but refreshing (kindly see highlihted part)
1690386646773.png


...this element ##r## can only be ##0## correct? The zero ring has only one element which is ##0##.
 
Physics news on Phys.org
Yes.
 
Thread 'How to define vector field?'

Thread 'How to define vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
View full post »

Similar threads

I What Is a Torsion Element in Ring Theory?
  • · Replies 13 ·
Replies
13
Views
3K
I Understanding zero divisors & ##\mathbb{Z_m}## in Ring Theory
  • · Replies 55 ·
2
Replies
55
Views
6K
I Definition of minimal ideal using symbolic logic notation
  • · Replies 3 ·
Replies
3
Views
866
I Localizing single variable quotient polynomial ring at a prime ideal
  • · Replies 6 ·
Replies
6
Views
1K
I Trouble with a passage in Zariski & Samuel's Commutative algebra text
  • · Replies 5 ·
Replies
5
Views
932
A Near-Rings with Noncommutative Addition and Two-Sided Distributivity
  • · Replies 4 ·
Replies
4
Views
2K
I Meaning of "identify" & variations in different math context
  • · Replies 5 ·
Replies
5
Views
789
I Meaning of "passage to the quotient"?
  • · Replies 3 ·
Replies
3
Views
727
MHB Notion of a ring with identity 1=0
  • · Replies 4 ·
Replies
4
Views
2K
MHB How to prove an ideal of a ring R which is defined as a coordinates
  • · Replies 1 ·
Replies
1
Views
1K