On the Amalgamated Duplication of an Unitary Normed Algebra Along an Ideal
-
2553
Downloads
-
3862
Views
Authors
Sara Dadras
- Department of Mathematics, Science and Research Branch, Islamic Azad University Tehran, Iran.
Mahsa Jafarian
- Department of Mathematics, Science and Research Branch, Islamic Azad University Tehran, Iran.
Abstract
In this paper, based on an amalgamated duplication of a ring along an ideal, we will construct the amalgamated duplication of an unitary normed algebra \(X\) along its proper ideal I (i.e. \(X \bowtie I\)). Then we will discus about its Banach conditions and abstract properties. Mainly we have proven that if \(X\) ba a Banach algebra and \(I\) be its closed ideal then \(X \bowtie I\) will be Banach algebra too. As well, we have shown that its completion and ideals based on original normed algebra \(X\). Finally some more aspects to expend these results for generalized normed algebras are given.
Share and Cite
ISRP Style
Sara Dadras, Mahsa Jafarian, On the Amalgamated Duplication of an Unitary Normed Algebra Along an Ideal, Journal of Mathematics and Computer Science, 8 (2014), no. 1, 75 - 80
AMA Style
Dadras Sara, Jafarian Mahsa, On the Amalgamated Duplication of an Unitary Normed Algebra Along an Ideal. J Math Comput SCI-JM. (2014); 8(1):75 - 80
Chicago/Turabian Style
Dadras, Sara, Jafarian, Mahsa. "On the Amalgamated Duplication of an Unitary Normed Algebra Along an Ideal." Journal of Mathematics and Computer Science, 8, no. 1 (2014): 75 - 80
Keywords
- Amalgamated duplication
- Unitary normed Algebra
- Banach Algebra
- *-algebra.
MSC
References
-
[1]
Akram B. Attar, Edge Extension Of Graphs And Digraphs, The Journal of Mathematics and Computer Science , 3 (2011), 1-10.
-
[2]
A. Bagheri, M. Salimi, E. Tavasoli, S. Yassemi, A construction of Quasi-Gorenstein rings, Journal of Algebra and Its Applications 1250013 , 11 (2012), 1-9.
-
[3]
J. A. Ball, H. Dym, M. A. Kaashoek, H. Langer, C. Tretter, The series in Operator Theory, Advances and Applications, springer ()
-
[4]
E. Tavasoli, M. Salimi, A. Tehranian , Amalagamted duplication of some special rings, Bull.Korean Math. Soc. , 49 (2012), 989-996.
-
[5]
H. Ananthnarayan, L. L. Avramov, W. Frank Moore, Conected sums of gorenstein local rings, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 667, arXiv:1005.1304v2 [math.AC] , 149–176 (2011)
-
[6]
J. Shapiro, On a construction of Gorenstein rings proposed by M. DAnna, Journal of Algebra , 323 (2010), 1155-1158.
-
[7]
Carlos S. Kubrusly, Elements of operator theory, Birkhäuser Boston, co Springer-Verlag , New York (1947)
-
[8]
M. D'Anna, A construction of Gorenstein rings , Journal of Algebra, 306 (2006), 507-519.
-
[9]
M. D'Anna, M. Fontana, An amalgamated duplication of a ring along an ideal, Journal of Algebra and Its Applications , 6 (2007), 443-459.
-
[10]
M. Nagata, Local Rings, Interscience, New York (1962)
-
[11]
M. Salimi, E. Tavasoli, S. Yassemi, The amalgamated duplication of a ring along a semidu-alizing ideal, Rend. Sem. Mat. Univ. , Padova Manoscritto in corso di stampa (2012)
-
[12]
M.Thill , Introduction to Normed *-Algebras and their Representations, 7th ed.arXiv:1011.1558v1 [math.OA] , (2010)
-
[13]
Y. Khomskii , Banach Algebras, Bachelor Thesis, (2005)