The element 0
is left-regular if and only if R
is trivial.
The element 0
is right-regular if and only if R
is trivial.
The element 0
is regular if and only if R
is trivial.
The element 0
is left-regular if and only if R
is trivial.
In a non-trivial MulZeroClass
, the 0
element is not left-regular.
The element 0
is right-regular if and only if R
is trivial.
In a non-trivial MulZeroClass
, the 0
element is not right-regular.
The element 0
is regular if and only if R
is trivial.
A left-regular element of a Nontrivial
MulZeroClass
is non-zero.
A right-regular element of a Nontrivial
MulZeroClass
is non-zero.
A regular element of a Nontrivial
MulZeroClass
is non-zero.
In a non-trivial ring, the element 0
is not left-regular -- with typeclasses.
In a non-trivial ring, the element 0
is not right-regular -- with typeclasses.
In a non-trivial ring, the element 0
is not regular -- with typeclasses.
Non-zero elements of an integral domain are regular.
In a non-trivial integral domain, an element is regular iff it is non-zero.