In an algebraic system, is there a general name for an element that behaves like 0 does for multiplication in $\mathbb R$?
129232
Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$?
34913
Why does basic algebra provide one value for $x$ when there should be two?
114609
Does the Banach algebra $L^1(\mathbb{R})$ have zero divisors?
154596
When should \cdot be used to indicate multiplication?
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
133495
Example of a ring without Invariant Basis Property
46010
Why don't we define division by zero as an arbritrary constant such as $j$?
22182
why don't we define vector multiplication component-wise?
88051
$\mathbb R = X^2$ as a Cartesian product
26055
Multiplication by $0$ in a field
95192
Other types of vector multiplication.
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
131844
When does $(e^a)^b = e^{ab}$ hold?
47015
Vector Space Structures over ($\mathbb{R}$,+)
22890
Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
66451
In a ring, how do we prove that a * 0 = 0?
40232
What do we mean when we say "Let $x$ be an element of the set $\mathbb{R}$"?