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An algebra of skew primitive elements [PDF]
Algebra and Logic, 1998 We study the various term operations on the set of skew primitive elements of Hopf algebras, generated by skew primitive semi-invariants of an Abelian group of grouplike elements. All 1-linear binary operations are described and trilinear and quadrilinear operations are given a detailed treatment.
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A proof of the conjecture of Cohen and Mullen on sums of primitive roots [PDF]
, 2014 We prove that for all $q>61$, every non-zero element in the finite field $\mathbb{F}_{q}$ can be written as a linear combination of two primitive roots of $\mathbb{F}_{q}$.
Cohen, Stephen D. +2 more
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Optimal primitive sets with restricted primes [PDF]
, 2013 A set of natural numbers is primitive if no element of the set divides another. Erd\H{o}s conjectured that if S is any primitive set, then \sum_{n\in S} 1/(n log n) \le \sum_{n\in \P} 1/(p log p), where \P denotes the set of primes.
Banks, William D., Martin, Greg
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Classification of finite dimensional irreducible modules over W-algebras [PDF]
, 2012 Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of characteristic 0) and its nilpotent element e.
Bernstein +20 more
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Primitive elements in free groups [PDF]
Proceedings of the American Mathematical Society, 1989 Let F n {F_n} denote the free group of rank n n generated by x 1 , x 2 , … , x n ...
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Advanced Intelligent Systems, 2020 Stateful logic enables highly energy‐efficient computation because the time and energy consumption for data transfer between the memory and the processing units in the traditional computation system can significantly be saved due to the combined ...
Nuo Xu +8 more
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PRIMITIVE ELEMENTS AND PREIMAGE OF PRIMITIVE SETS OF FREE LIE ALGEBRAS [PDF]
International Journal of Pure and Apllied Mathematics, 2014 Let F and L be free Lie algebras of finite rank n andm respectively and φ be a homomorphism from F to L. We prove that the preimage of a primitive set of L contains a primitive set of F . As a consequence of this result we obtain that an element h of a subalgebra H of F is primitive in H if it is primitive in F . Also we show that in a free Lie algebra
Ersalan D., Esmerligil Z.
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On primitive elements in finite semifields
Finite Fields and Their Applications, 2011 Semifields \((S,+,\cdot)\) in the meaning of this article are division rings with identity, where the multiplication is not necessarily associative. The centre of such a semifield is defined as \(K=\{ a\in S\mid (ab)c=a(bc), b(ac)=(ba)c, b(ca)=(bc)a, ab=ba\) for all \(b,c\in S\}\). If \(S\) is a finite semifield then its centre is a finite field \(F_q\)
Rod Gow, John Sheekey
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Computing Multiplicative Order and Primitive Root in Finite Cyclic Group
, 2014 Multiplicative order of an element $a$ of group $G$ is the least positive integer $n$ such that $a^n=e$, where $e$ is the identity element of $G$. If the order of an element is equal to $|G|$, it is called generator or primitive root.
Dwivedi, Shri Prakash
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The transformations of the concept of fate in literature
Scripta Instituti Donneriani Aboensis, 1967 In the course of time the literary idea of fate has been subject to a series of transformations which may also be of some interest from the point of view of comparative religion.
Mogens Bröndsted
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