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if a and x are in A such that ax ≤ x, then a * x ≤ x; if a and x are in A such that xa ≤ x, then x(a *) ≤ x; Intuitively, one should think of a + b as the "union" or the "least upper bound" of a and b and of ab as some multiplication which is monotonic, in the sense that a ≤ b implies ax ≤ bx. The idea behind the star operator is a ...
In this case 8 times 365 is 2920 and further addition of multiples of 365 would clearly give a value greater than 3200. Next it is noted that 2 / 3 + 1 / 10 + 1 / 2190 times 365 gives us the value of 280 we need. Hence we find that 3200 divided by 365 must equal 8 + 2 / 3 + 1 / 10 + 1 / 2190 . [8]
In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power.Exponentiation is written as b n, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n ". [1]
According to the Artin–Wedderburn theorem a finite-dimensional simple algebra A is isomorphic to the matrix algebra M(n,S) for some division ring S. Hence, there is a unique division algebra in each Brauer equivalence class. [3] Every automorphism of a central simple algebra is an inner automorphism (this follows from the Skolem–Noether ...
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation" [3]) is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentiable manifolds, numerical analysis, number theory, calculus and statistics.
Let V and W be vector spaces over a field (or more generally, modules over a ring) and let T be a linear map from V to W.If 0 W is the zero vector of W, then the kernel of T is the preimage of the zero subspace {0 W}; that is, the subset of V consisting of all those elements of V that are mapped by T to the element 0 W.
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method.The word FOIL is an acronym for the four terms of the product:
More generally, one can construct the free algebra R E on any set E of generators. Since rings may be regarded as Z-algebras, a free ring on E can be defined as the free algebra Z E . Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space.
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