Updating the Fundamental Theorem of Homomorphism of General Universal Algebras
Keywords:
Algebra of a given type, Homomorphisms, Kernel of a homomorphism, Congruence Relations and an associate of a homomorphism.Abstract
From the fundamental theorem of homomorphisms, it is well known that any homomorphism of groups (or rings, or modules, or vector spaces and of general universal algebras) can be decomposed as a composition of a monomorphism and an epimorphism. This paper provides the uniqueness of such decomposition up to the level of associates in the case of general universal algebras
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[2] Clifford Bergman, Universal Algebra: Fundamentals and Selected Topics, CRC Press, 2011
[3] Gertude Ehrlich, Fundamental Concept of Abstract Algebra, Courier Corporation, 2013
[4] Jacobson, N., Basic Algebra-Vol I, W. H. Freeman, San Francisco, 1980
[5] Jonathan K. Hodge, Steven Schlicker, Ted Sundstrom, Abstract Algebra: An Inquiry Based Approach, CRC Press, 2013
[6] Klaus Denecke, Shelly L. Wismath, Universal Algebra and Coalgebra: World Scientific, 2009
[7] Klaus Denecke, Shelly L. Wismath, Universal Algebra and Applications in Theoretical Computer Science: CRC Press, 2002 [P 47-63]
[8] L. Szabó, A. SzendreiLectures in Universal Algebra, Volume 1 of Colloquia MathematicaSocietatis Janos Bolyai , Elsevier, 2014
[9] Paul B. Garrett, Abstract Algebra, CRC Press, 2007 (page25-56)
[10] Peter Hilton, Yel-Chiang Wu, A Course in Modern Algebra: Pure and applied mathematics
Volume 12 of Wiley Classics Library, John Wiley & Sons, 1989
[11] Pierce, R.S., Introduction to the theory of Abstract Algebra, Halt, Rinehart and winston, New York, 1968
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Published
2014-09-21
How to Cite
Addis, G. M. (2014). Updating the Fundamental Theorem of Homomorphism of General Universal Algebras. American Scientific Research Journal for Engineering, Technology, and Sciences, 10(1), 61–73. Retrieved from https://www.asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/707
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