MATHEMATICAL STRUCTURES DEFINED
BY IDENTITIES III

Abstract

We extend the theory (formal part only) of algebras with one binary operation (our paper, Petridi [#!Petridi1!#]) to algebras with several operations of any arity.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 5
Year: 2019

DOI: 10.12732/ijam.v32i5.7

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] M. Aigner, Catalan and Other Numbers: A Recurrent Theme, Algebraic Combinatories and Computer Science, Springer (2001).
  2. [2] J. Baez, J. Dolan, Higher-dimensional Algebra III: n-categories and the algebra of opetopes, Adv. Math. 135 (1998), 145-206.
  3. [3] Yu.R. Bakhturin, A.Yu. Ol’shankij, Identities, Encyclopaedia of Mathematical Sciences, Vol. 18, Algebra II, Springer (1991).
  4. [4] B.C. Berndt, Ramanujan’s Notebooks, Part I, Springer (1985).
  5. [5] P.M. Cohn, Universal Algebra, Harper & Row (1965).
  6. [6] L.E. Dickson, History of the Theory of Numbers. Vol. II: Diophantine Analysis, Dover (2005).
  7. [7] D.H. Lehmer, Computer Technology Applied to the Theory of Numbers, In: Studies in Number Theory, 6 (1969), l17-l5l.
  8. [8] C.M. Petridi, Mathematical structures defined by identities, arXiv:math/0110333v1 [math.RA] 31 Oct 2001, 31 pp.
  9. [9] C.M. Petridi, Mathematical structures defined by identities, II, arXiv:math/1009.1006v1 [math.RA] 6 Sep 2010, 6 pp.
  10. [10] J. Riordan, Combinatorial Identities, J. Wiley (1968).
  11. [11] A. Tarski, Equational Logic and Equational Theories of Algebras, Studies in Logic and the Foundations of Mathematics, Elsevier (1968).
  12. [12] H. Wilf, Generating Functionology, Academic Press (1990).