lattice may sometimes be called a zero element, and written either as 0 or ⊥. 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. Zero ideal In mathematics, the zero ideal in a ring is the ideal consisting of only the additive identity (or zero element). The fact that this is an ideal follows directly from the definition. Zero matrix In mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero. It is alternately denoted by the symbol . Some examples of zero matrices are The set of m × n matrices with entries in a ring K forms a module . The zero matrix in is the matrix with all entries equal to , where is the additive identity in K. The zero matrix is the additive identity in . That is, for all : There is exactly one zero matrix of any given size m × n (with entries from a given ring), so when the context is clear, one often refers to the zero matrix. In general, the zero element of a ring is unique, and typically denoted as 0 without any subscript to indicate the parent ring. Hence the examples above represent zero matrices over any ring. The zero matrix also represents the linear transformation which sends all vectors to the zero vector. Zero tensor In mathematics, the zero tensor is a tensor, of any order, all of whose components are zero. The zero tensor of order 1 is sometimes known as the zero vector. Taking a tensor product of any tensor with any zero tensor results in another zero tensor. Adding the zero tensor is equivalent to the identity operation. See also Null semigroup Zero divisor Zero object Zero of a function Zero — non-mathematical uses References 0 (number)