Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An embedding theorem for matrices of commutative cancellative semigroups
HTML articles powered by AMS MathViewer

by James Streilein PDF
Trans. Amer. Math. Soc. 208 (1975), 127-140 Request permission

Abstract:

In this paper it is shown that each semigroup which is a matrix of commutative cancellative semigroups has a “quotient semigroup” which is a completely simple semigroup with abelian maximal subgroups. This result is proved by explicitly constructing the quotient semigroup. The paper also gives necessary and sufficient conditions for a semigroup of the type being considered in the paper to be isomorphic to a Rees matrix semigroup over a commutative cancellative semigroup. Several special cases and examples are also briefly discussed.
References
  • Ernst-August Behrens, Ring theory, Pure and Applied Mathematics, Vol. 44, Academic Press, New York-London, 1972. Translated from the German by Clive Reis. MR 0379551
  • Ernst-August Behrens, The arithmetic of the quasi-uniserial semigroups without zero, Canadian J. Math. 23 (1971), 507–516. MR 285459, DOI 10.4153/CJM-1971-054-6
  • A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
  • Robert P. Dickinson Jr., On right zero unions of commutative semigroups, Pacific J. Math. 41 (1972), 355–364. MR 306362, DOI 10.2140/pjm.1972.41.355
  • Robert E. Hall, The translational hull of an $N$-semigroup, Pacific J. Math. 41 (1972), 379–389. MR 306369, DOI 10.2140/pjm.1972.41.379
  • Mario Petrich, Introduction to semigroups, Merrill Research and Lecture Series, Charles E. Merrill Publishing Co., Columbus, Ohio, 1973. MR 0393206
  • Mario Petrich, Normal bands of commutative cancellative semigroups, Duke Math. J. 40 (1973), 17–32. MR 311819
    • J. Shafer, Homomorphisms and subdirect products of free contents (unpublished).
  • Takayuki Tamura, Commutative nonpotent archimedean semigroup with cancelation law. I, J. Gakugei Tokushima Univ. 8 (1957), 5–11. MR 96741
    • —, The study of closets and free contents related to the semi-lattice decomposition of semigroups, Semigroups (Proc. Sympos., Wayne State Univ., Detroit, Mich., 1968), Academic Press, New York, 1969, pp. 221-260. MR 46 #5504.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 20M10
  • Retrieve articles in all journals with MSC: 20M10
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 208 (1975), 127-140
  • MSC: Primary 20M10
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0374306-9
  • MathSciNet review: 0374306