Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Grushko-like theorems for a class of finitely presented semigroups


Author: Ann Yasuhara
Journal: Proc. Amer. Math. Soc. 42 (1974), 359-364
MSC: Primary 20M05
DOI: https://doi.org/10.1090/S0002-9939-1974-0335665-0
MathSciNet review: 0335665
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An analogue of Grushko's theorem and the unsolvability of the isomorphism problem hold for semigroups in the class of all finitely presented semigroups that have a presentation in which there is no defining relation of the form $ 1 \Leftrightarrow A$; this class is not recursive but is recursively enumerable.


References [Enhancements On Off] (What's this?)

  • [C&P] A. H. Clifford and G. B. Preston, The algebraic theory of semi-groups, Vol. II, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1967. MR 36 #1558. MR 0218472 (36:1558)
  • [D] M. Davis, Computability and unsolvability, McGraw-Hill Series in Information Processing and Computers, McGraw-Hill, New York, 1958. MR 23 #A1525. MR 0124208 (23:A1525)
  • [K] A. G. Kuroš, Theory of groups, GITTL, Moscow, 1953; English transl., Vol II, Chelsea, New York, 1960. MR 15, 501; 22 #727.
  • [M] A. A. Markov, The theory of algorithms, Trudy Mat. Inst. Steklov. 42 (1954); English transl., Israel Program for Scientific Translations, Jerusalem, 1961. MR 17, 1038; 24 #A2527. MR 0132690 (24:A2527)
  • [MK&S] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617. MR 0207802 (34:7617)
  • [Mo] A. Mostowski, Review of A. A. Markov's impossibility of algorithms for recognizing some properties of associative systems, J. Symbolic Logic 17 (1952), p. 151.
  • [R] M. O. Rabin, Recursive unsolvability of group theoretic problems, Ann. of Math. (2) 67 (1958), 172-194. MR 22 #1611. MR 0110743 (22:1611)
  • [Y1] A. Yasuhara, Recursive function theory and logic, Academic Press, New York, 1971. MR 0313027 (47:1582)
  • [Y2] -, Some non-recursive classes of semi-groups with solvable word problem, Z. Math. Logik Grundlagen Math. (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20M05

Retrieve articles in all journals with MSC: 20M05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0335665-0
Keywords: Finitely presented semigroup, free product, rank, decision problem
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society