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A zero element (or an absorbing/annihilating element) is an element z such that for all s in S, z • s = s • z = z. This notion can be refined to the notions of left zero, where one requires only that z • s = z, and right zero, where s • z = z. [2]
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. The fact that this is an ideal follows directly from the definition.
The role of 0 as additive identity generalizes beyond elementary algebra. In abstract algebra, 0 is commonly used to denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined). (Such elements may also be called zero elements.)
The zero ring consisting only of a single element 0 = 1 is a terminal object. In Rig, the category of rigs with unity and unity-preserving morphisms, the rig of natural numbers N is an initial object. The zero rig, which is the zero ring, consisting only of a single element 0 = 1 is a terminal object.
A branch of biology concerned with the computational and mathematical analysis of complex biological systems. It is an interdisciplinary field which combines elements of systems theory and applied mathematics with theoretical biology, with a primary aim to discover and model the emergent properties of interacting biological entities.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
Under zero-based numbering, the initial element is sometimes termed the zeroth element, [1] rather than the first element; zeroth is a coined ordinal number corresponding to the number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element ...
Neutronium (or neutrium, [1] neutrite, [2] or element zero) is a hypothetical substance made purely of neutrons.The word was coined by scientist Andreas von Antropoff in 1926 (before the 1932 discovery of the neutron) for the hypothetical "element of atomic number zero" (with no protons in its nucleus) that he placed at the head of the periodic table (denoted by -).