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The handle http://hdl.handle.net/1887/40676 holds various files of this Leiden University dissertation.

Author: Ciocanea Teodorescu, I.

Title: Algorithms for finite rings Issue Date: 2016-06-22

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List of symbols

Fq finite field withq elements

Z ring of integers

Z>0 set of positive integers Z≥0 set of non-negative integers

|S| cardinality of a setS

Mn(R) ring ofn × n matrices with entries in the ring R Mn×m(R) set ofn × m matrices with entries in the ring R Re the enveloping algebra ofR (page 76)

Ro the opposite ring of the ring R R[G] the group ring ofG over R

Max(R) set of maximal ideals of a commutative ring R Spec(R) set of prime ideals of a commutative ringR J(R) Jacobson radical of a ring R

Z(R) centre of a ringR

char(R) characteristic of a ringR

rad(n) the product of all primes dividing an integern

,→ injective map

 surjective map

M ⊗RN tensor product ofM with N over R EndR(M ) ring ofR-endomorphisms of M

HomR(M, N ) group ofR-homomorphisms from M to N MfgR category of finitely generated rightR-modules MR category of rightR-modules

v

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vi Algorithms for finite rings

fg

RM category of finitely generated leftR-modules

RM category of leftR-modules

RMS R-S-bimodule M

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From 1997 to 2004 she was simultaneously a student of the Goethe German College and the George Enescu Music High School (piano studies), in Bucharest (Romania).. In 2009 she