International Research journal of Management Science and Technology

  ISSN 2250 - 1959 (online) ISSN 2348 - 9367 (Print) New DOI : 10.32804/IRJMST

Impact Factor* - 6.2311


**Need Help in Content editing, Data Analysis.

Research Gateway

Adv For Editing Content

   No of Download : 181    Submit Your Rating     Cite This   Download        Certificate

SOME COMMUTATIVITY THEOREMS FOR RINGS WITHOUT UNITY

    1 Author(s):  DR. SUMAN GUPTA

Vol -  8, Issue- 8 ,         Page(s) : 302 - 306  (2017 ) DOI : https://doi.org/10.32804/IRJMST

Abstract

This study persues to create new mathematics form an existing mathematical theory specially one presented in an axiomatic form is to generalize the theory by dropping or weakening some of its hypothesis Analogous to the symmetric group of permutations algebra of linear transformation of a vector space was studied and it was found that it does not satisfy the cummutative property xy=yx in general mathematicians like J.J. Graves. A Caley, Sophus Lie and P. Jordan Introduced more general types of algebras which do not satisfy associative law, namely (xy) z=x(yz) When these non- cummutative and non-associative algebras were introduced traditional mathematicians did not give them more importance than that of ‘FICTIONS’

1.       Abujabal, H.A.S. A generalization of some commutatinity the orems for rings I tamking J.Math 21 (1990), 1-7.
2. Achlesh Kumari and Nadeem-ur Rehman A remak on strongly co-commutativity preseving endomorphisms, Aligarh Bull, of Maths. 17 (1997-98)
3. Ashraf, M and M.A. Quadri A note on commutativity of rings Communication de la Faculte des I ‘Universite d’ Anpara 34 (1987) 1-3.
4. Abujabal, H.A.S. and M. Obaid: Some commutatinity the orens far right 6-unital rings Math. Taponica, 37(1992), 591-600.
5. Abujabal, H.A.S. and V. Peric: commis Aativity of S-unital rings through a sterb result, Road, Math, 7 (1991), 73-92
6. Bell, H.E. : Duo rings : some applications to Commutavity theorems, Canad, Math Bull. 11 (1968), 375-380.
7.   Bell, H.E. : A commutativity condition for rings, Canad J Math, 28 (1976). 986-991.
8.    Bell, H.E. : On rings with commuting powers, Math Japonica 27 (1979). 473-478.
9. Herstien: Ring with Invalution University Chicago Press, Chicago-1976.
10. Hirano, Y: Two Theorems on left S-unital Math J. Okayama Univ. 20 (1978), 67-72.
11. Hirano,Y, Y. Kobayashi and H.Tominaga: Some Polynominal identities and commutativity of s-unital rings,Math.J. Okayama univ. 24(1982),7-13.
12. Herstein I.N. : A condition for the commutativity of rings. Canad. J. Math 9 (1957) (1955), 583-586.
13. Herstein I.N. : Power map in rings Michigan Math. J 8 (1961), 29-32.
14.   Jacobson. N. : Structure theory of algebraic algebras of bounded degree, Ann, Math. 46 (1945), 695-707.
15. Johnsen, E.C., D.c. Outcalt and A Yaqub : An elementary commutavity theorem for rings. Amer. Math. Monthly 75 (1968), 288-289.
16.     Kamatsu, H. and H. Tominaga, some commutinity therms for left S-united rings, result Math. 15 ()1989, 335-342.
17. Psomopoulos, E.H. Tominaga and A yaqub : some communativity theorems for n-torsion free rings, Math. J. Okayama Univ. 23 (1981), 37-39.
18. Ligh, S. and J. Luch : Some commutativity theorems for rings and near rings, Acta Math Acad. Sci. Hungar, 28 (1976), 19-23
19. Quadri M.A., Asma Ali and Achlesh Kumari : On commutativity of certain Periodic rings, Proceedings of the fourth Ramanujan symposium on Algebra and its applications (1995).
20.   Tominaga, H. : On s-unital rings, Math. J. Okayama Univ. 19 (1976), 117-136.
21. Tominaga, H and A Yaqub : some commutatinity conditions for left s-unital rings satisfying certain paly nomial identities result. Math 6 (1983), 217-219.
22. Tominaga, H : A Commutativity thheorem for one sided s-unital rings, Math. J. Okayama Univ. 26 (1984), 125-128.
23. Tong, J. A commutativity The aren for one sided S-unital rings, Math. J. Okayama Univ. 26 (1984), 125-128.

*Contents are provided by Authors of articles. Please contact us if you having any query.






Bank Details