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In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, =, = = This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties. [1]
Note also how multiplication by zero causes a reduction in dimensionality, as does multiplication by a singular matrix where the determinant is 0. In this process, information is lost and cannot be regained. For real and complex numbers, which includes, for example, natural numbers, integers, and fractions, multiplication has certain properties:
Distinguished class A class C of field extensions with the three properties [17] If E is a C-extension of F and F is a C-extension of K then E is a C-extension of K. If E and F are C-extensions of K in a common overfield M, then the compositum EF is a C-extension of K. If E is a C-extension of F and E > K > F then E is a C-extension of K.
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 -).
A motivating example that is neither a ring nor a lattice is the set of natural numbers (including zero) under ordinary addition and multiplication. Semirings are abundant because a suitable multiplication operation arises as the function composition of endomorphisms over any commutative monoid .
The Egyptians used the commutative property of multiplication to simplify computing products. [7] [8] Euclid is known to have assumed the commutative property of multiplication in his book Elements. [9] Formal uses of the commutative property arose in the late 18th and early 19th centuries, when mathematicians began to work on a theory of ...
Atomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions, at the scale of one or a few atoms [1] and energy scales around several electron volts. [2]: 1356 [3] The three areas are closely interrelated. AMO theory includes classical, semi-classical and quantum treatments.
Exotic matter is a concept of particle physics, which may include dark matter and dark energy but goes further to include any hypothetical material that violates one or more of the properties of known forms of matter.
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