Zero element partially coincident with identity element
The empty set, which is an absorbing element under Cartesian product of sets, since { } × S = { }
The zero function or zero map defined by z(x) = 0 under pointwise multiplication (f ⋅ g)(x) = f(x) ⋅ g(x)Many absorbing elements are also additive identities, including the empty set and the zero function. Another important example is the distinguished element 0 in a field or ring, which is both the additive identity and the multiplicative absorbing element, and whose principal ideal is the smallest ideal.The trivial group, containing only the identity (a zero object in the category of groups)
The zero module, containing only the identity (a zero object in the category of modules over a ring)Zero module
In mathematics, the zero module is the module consisting of only the additive identity for the module's addition function. In the integers, this identity is zero, which gives the name zero module. That the zero module is in fact a module is simple to show; it is closed under addition and multiplication trivially.
partially overlapping with partially intersecting with partially sharing with partially matching with partially aligning with