Non-commutative multiplicationPublic-key cryptographyPost-quantum cryptographyDigital signatureThere are introduced three methods for defining finite 6-dimensional associative algebras over the ground finite field GF(p), every one of which contains a set of the global right-sided units. Formulas describing...
, gen- eralizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non- commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms. 57M27; 57N10 1...
The Pauli algebra P, in which the usual dot and cross products of 3-space vectors are combined in an associative, invertible, but non-commutative multiplication, provides a simple but powerful approach to problems in special relativity. ... WE Baylis,G Jones - 《Journal of Physics A General...
On the non-commutative Main Conjecture for elliptic curves with complex multiplication In [7] a non-commutative Iwasawa Main Conjecture for elliptic curves over Q has been formulated. In this note we show that it holds for all CM-elliptic cur... T Bouganis,O Venjakob - 《Asian Journal of ...
Ondrej Sy´kora: A fast non-commutative algorithm for matrix multiplication, In Mathematical foundations of computer science (Proc. Sixth Sympos., Tatransk´a Lomnica, 1977), Springer, 1977, p. 504512. LNCS 53.Sykora, O. A fast non-commutative algorithm for matrix multiplica- tion. In ...
什么是非交换几何(非交换拓扑)(What is non-commutative geometry (non-switching topology)) At the Christmas party, someone asked me what the geometry was. I regret that I had given a huge, bullshit explanation, so now Im reinterpreting it as compensation for more than one person. Because I on...
We shall consider non-associative and non-commutative pseudo-addition and pseudo-multiplication, i.e., generalized pseudo-operations. More precise, we shall consider special class of generalized pseudo-operations that have the following form: x⊕ y=k-1(ε k(x)+k(y)), x⊙ y=k-1(k(x)ε...
In this case their computation is not asymptotically fast, but once obtained, they may be used to compute multiple quotients, each with one multiplication. Examples are shown of polynomials with matrix coefficients, differential operators and difference operators. In addition, a proof-of-concept ...
The idealization (trivial extension) 𝑅⋉𝑀={(𝑟,𝑚):𝑟∈𝑅,𝑚∈𝑀}R⋉M={(r,m):r∈R,m∈M} of M is a ring with component wise addition defined by: (𝑥,𝑚1)+(𝑦,𝑚2)=(𝑥+𝑦,𝑚1+𝑚2)(x,m1)+(y,m2)=(x+y,m1+m2) and multiplication is ...
Note that multiplication of superfields are defined by the ∗-product. This Lagrangian is invariant under the gauge transformations Φ→e −iΛ ∗Φ∗e iΛ , ¯ Φ→ e −i ¯ Λ ∗ ¯ Φ∗e i ¯ Λ and e V →e −i ¯ Λ ∗e V ∗e iΛ . To ...