**" Common Region between Associative Algebras and Non-Associative Lie Algebras " ,**

**Mehsin Jabel Atteya ... 2017, No.2 , P.27 - 32**

**DOI : http://dx.doi.org/10.22039/cjcme.2017.06**

**Abstract:**

**The main purpose of this note is to introduce associative algebra ring and non-associative Lie algebra have a common region. Of this common region we present the area which is commutative.**

**References :**

**1. N. C. Hopkins, Quadratic differential equations in graded algebras. In Nonassociative Algebra and its Applications (S. Gonzálezed.), Math. Appl. 303, Kluwer Acad. Publ.,(1994), pp. 179–182.**

**2. L. Markus, Quadratic differential equations and non-associative algebras, Annals of Math. Stud., 45, (1960), pp. 185–213.**

**3. A. Elduque and H.C. Myung, The reductive pair (B4, B3) and affine connections on S15. J. Algebra 227, no. 2, (2000), pp.504–531, 2000.**

**4. M. L. Reed, Algebraic structures of genetic inheritance. Bull. Amer. Math. Soc.34, (1997), pp.107–130.**

**5. R. Iordanescu, The associativity in present mathematics and present physics, presentation – Bucharest, 2014.**

**6. R. Iordanescu, 2011, arXiv preprint math-DG/1106.4415.**

**7. C. Brian Hall, Lie groups, Lie algebras, and Representations, An Elementary Introduction, Graduate Texts in Mathematics, Springer-Verlag New York, Inc., 2003.**

**8. Frank W. Anderson, Lectures on non-commutative rings, Mathematics 681 University of Oregon, Oregon, 2002.**