Some properties of quasiassociative and quasialternative algebras Let A be an algebra over a field F, and λ∈F be an arbitrary fixed element. Then A (λ) denotes the algebra obtained by defining a new multiplication a* λ b=λab+(1-λ)ba on the vector space A. An algebra A is cal...
The extra generality of the extensions we consider over bounded extensions has two immediate advantages: firstly, it allows the extension \(B\leqslant A\) to be “ large”, in the sense that the tensor algebra T[B, A/B] can have arbitrarily long non-zero words \(v_1\otimes \ldots ...
Abstract We study a class of matrices with noncommutative entries, which were first considered by Yu.I. Manin in 1988 in relation with quantum group theory. They are defined as “noncommutative endomorphisms” of a polynomial algebra. More explicitly their defining conditions read: (1) elements ...
It is shown that the maximal Lie algebra of a first integral for the simplest equation y???=0 is unique and four-dimensional. Moreover, we show that the Lie algebra of the simplest linear third-order equation is generated by the symmetries of the two basic integrals. We also obtain count...
The standard for of representation of a cubic equation is \(a{x^3} + b{x^2} + cx + d = 0.\)Abstract AlgebraAbstract algebra operates using abstract concepts like rings, groups, vectors rather than simple mathematical number systems. Ring theory and group theory are two important areas ...
Galois group containing A n . It should be noted that reducible GLP for rational values of the parameter α do exist (already infinitely many exist in degrees 2, 3 or 4, cf. Section 6). The irreducibility part of the above theorem is due to Filaseta and Lam [FL]; the supplement ...
In this section, we give some generalizations of pre-topological groups, such as, semi-pre-topological groups, quasi-pre-topological groups and para-pre-topological groups. Moreover, we study some basic properties of them. Definition 4.1 Let τ be a pre-topology on a group G. We say that...
摘要: Some properties of finite groups are proved. The no- tion of cyclic group is defined next, some cyclic groups are given, for example the group of integers with addition operations. Chosen proper- ties of cyclic groups are proved next.关键词:...
2007, Journal of Pure and Applied Algebra Show abstract A classic result of Swan states that a finite groupGacts freely on a finite homotopy sphere if and only if every abelian subgroup ofGis cyclic. Following this result, Benson and Carlson conjectured that a finite groupGacts freely on a...
Abstract Our main goal is to present new representations and properties of the m-weak group inverse which presents a generalization of the weak group inverse, the generalized group inverse, the group inverse and the Drazin inverse. Consequently, we obtain new properties of the generalized group inv...