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Cornish Mutual is a general insurer based in Cornwall, set up by Cornish farmers in 1903.The company is based in Truro. [4]The mutual is owned by its members and offers insurance to farms, businesses and people living and working in Cornwall, Devon, Somerset and Dorset.
[15] From 1967 to 1969, Kaplansky wrote the mathematics section of Encyclopædia Britannica. [16] [17] [18] Kaplansky was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986. [19] Kaplansky was also an accomplished amateur musician.
Kaplansky's zero divisor conjecture states: The group ring K[G] does not contain nontrivial zero divisors, that is, it is a domain. Two related conjectures are known as, respectively, Kaplansky's idempotent conjecture: K[G] does not contain any non-trivial idempotents, i.e., if a 2 = a, then a = 1 or a = 0.
In abstract algebra, Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is free; [1] where a not-necessarily-commutative ring is called local if for each element x, either x or 1 − x is a unit element. [2]
People named Kaplansky (Polish: Kapłański (feminine Kapłańska), Russian: Капланский, also Kaplanski (feminine Kaplanska)) include: Abraham Kaplansky (1860–1939), Canadian printer; Kalmen Kaplansky (1912–1997), Canadian labour and human rights activist; Irving Kaplansky (1917–2006), Canadian mathematician Kaplansky density ...
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Five results similar to Kaplansky's theorem are known: [3] A prime p congruent to 1 modulo 20 is representable by both or none of x 2 + 20y 2 and x 2 + 100y 2, whereas a prime p congruent to 9 modulo 20 is representable by exactly one of these quadratic forms.
For instance, the surjectivity part implies the Kadison–Kaplansky conjecture for discrete torsion-free groups, and the injectivity is closely related to the Novikov conjecture. The conjecture is also closely related to index theory , as the assembly map μ {\displaystyle \mu } is a sort of index, and it plays a major role in Alain Connes ...