Wang, "Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative
Rings," IACR Cryptol.
Majid, Physics for algebraists: Non-commutative
and non-cocommutative Hopf algebras by a bicrossproduct construction.
Moreover, authors noticed that the main problem for construction of cryptographic primitives in infinite non-commutative
groups is to reliably hide the factors in group word.
They cover both commutative and non-commutative
2009, Super, Quantum and Non-Commutative
6) Spec o G is a contravariant graded functor from the category of non-commutative
Zariski filtered rings with units and strict epimorphisms to the category of topological (graded) spaces and continuous maps.
geometry unites the non-commutative
operators of quantum mechanics and the geometrical objects of general relativity.
the ring of polynomials is now a non-commutative
ring of twisted polynomials, defined over the differential field of meromorphic functions in system variables,
Lanski proved that if R is a prime ring, L a non-commutative
Lie ideal of R and g [not equal to] 0 a derivation of R, such that [g(x), x] [member of] Z(R), for all x [member of] L, then either R is commutative, or char(R) = 2 and R satisfies [s.
mu]] obey the non-commutative
Yang's space time algebra.
Then he moves into much more advanced terrain, dealing with how to set up working Monte Carlo simulations of matrix field theories, which involve finite dimensional matrix regularizations of non-commutative
and fuzzy field theories, fuzzy spaces, and matrix geometry.
Mathematically, quantum information theory extends Shannon~s theory of information but differs from it by allowing both for stronger correlations known as entanglement and for non-commutative
effects resulting in measurement uncertainty as required by the laws of quantum physics.