Rings with left self distributive multiplication

1992 ◽  
Vol 60 (1-2) ◽  
pp. 107-114 ◽  
Author(s):  
G. F. Birkenmeier ◽  
H. Heatherly ◽  
T. Kepka
Keyword(s):  
Distributive Multiplication

scholarly journals Semirings with a completely simple additive semigroup

1975 ◽  
Vol 20 (3) ◽  
pp. 257-267 ◽  
Author(s):  
Mireille P. Grillet
Keyword(s):  
Additive Semigroup ◽  
Completely Simple ◽  
Distributive Multiplication

We construct all semirings with a given completely simple additive semiroup ℳ(G, I, ∧, P) by means of an associative and distributive multiplication on G, and associative multiplications on I and ∧ satisfying certain conditions.

Distributive multiplication rings

1992 ◽  
Vol 25 (2) ◽  
pp. 161-165 ◽  
Author(s):  
S. Feigelstock ◽  
R. Raphael
Keyword(s):  
Distributive Multiplication

scholarly journals A Three Dimensional Modification of the Gaussian Number Field

2019 ◽  
Vol 74 (1) ◽  
pp. 63-76
Author(s):  
Ján Haluška ◽  
Małgorzata Jastrzębska
Keyword(s):  
Number Field ◽  
Associative Algebra ◽  
Direct Product ◽  
Complex Plane ◽  
Three Dimensional ◽  
Complex Numbers ◽  
Geometrical Properties ◽  
Hyperbolic Complex ◽  
Algebra Over A Field ◽  
Distributive Multiplication

Abstract For vectors in E3 we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and hint some applications. Based on properties of hyperbolic (Clifford) complex numbers, we prove that the resulting algebra 𝕋 is an associative algebra over a field and contains a subring isomorphic to hyperbolic complex numbers. Moreover, the algebra 𝕋 is isomorphic to direct product ℂ×ℝ, and so it contains a subalgebra isomorphic to the Gaussian complex plane.

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