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Eureka has been published 66 times since 1939, and authors include many famous mathematicians and scientists such as Paul Erdős, Martin Gardner, Douglas Hofstadter, G. H. Hardy, Béla Bollobás, John Conway, Stephen Hawking, Roger Penrose, W. T. Tutte (writing with friends under the pseudonym Blanche Descartes), popular maths writer Ian ...
A first date is the initial meeting during the dating process of two individuals, in which an effort is made to ask about each other, plan a potential relationship, and/or organize some sort of romantic activity. Aims vary between finding a romantic, platonic, or sexual partner for a short period, to finding a long-term spouse.
A two-sided ideal of a ring R can also be called a (von Neumann) regular ideal if for each element x of there exists a y in such that xyx=x. [ 4 ] [ 5 ] Finally, regular ideal has been used to refer to an ideal J of a ring R such that the quotient ring R / J is von Neumann regular ring . [ 6 ]
An ideal whose radical is maximal, however, is primary. Every ideal Q with radical P is contained in a smallest P-primary ideal: all elements a such that ax ∈ Q for some x ∉ P. The smallest P-primary ideal containing P n is called the n th symbolic power of P. If P is a maximal prime ideal, then any ideal containing a power of P is P-primary.
The first algorithm for computing primary decompositions for polynomial rings over a field of characteristic 0 [Note 1] was published by Noether's student Grete Hermann . [1] [2] The decomposition does not hold in general for non-commutative Noetherian rings. Noether gave an example of a non-commutative Noetherian ring with a right ideal that ...
Eureka comes from Ancient Greek εὕρηκα (heúrēka) 'I have found (it)', which is the first person singular perfect indicative active of the verb εὑρίσκω heurískō ' I find '. [1] It is closely related to heuristic, which refers to experience-based techniques for problem-solving, learning, and discovery.
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
A Hasse diagram of the divisors of , ordered by the relation is divisor of, with the upper set colored green. The white sets form the lower set . In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) [1] of a partially ordered set (,) is a subset with the following property: if s is in S and if x in X is larger than s (that is, if <), then x is in S.