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Transactions of the American Mathematical Society

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An embedding theorem for matrices of commutative cancellative semigroups

Author: James Streilein
Journal: Trans. Amer. Math. Soc. 208 (1975), 127-140
MSC: Primary 20M10
MathSciNet review: 0374306
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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.

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  • [1] Ernst-August Behrens, Ring theory, Academic Press, New York-London, 1972. Translated from the German by Clive Reis; Pure and Applied Mathematics, Vol. 44. MR 0379551
  • [2] Ernst-August Behrens, The arithmetic of the quasi-uniserial semigroups without zero, Canad. J. Math. 23 (1971), 507–516. MR 0285459,
  • [3] 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
  • [4] Robert P. Dickinson Jr., On right zero unions of commutative semigroups, Pacific J. Math. 41 (1972), 355–364. MR 0306362
  • [5] Robert E. Hall, The translational hull of an 𝑁-semigroup, Pacific J. Math. 41 (1972), 379–389. MR 0306369
  • [6] Mario Petrich, Introduction to semigroups, Charles E. Merrill Publishing Co., Columbus, Ohio, 1973. Merrill Research and Lecture Series. MR 0393206
  • [7] Mario Petrich, Normal bands of commutative cancellative semigroups, Duke Math. J. 40 (1973), 17–32. MR 0311819
  • [8] J. Shafer, Homomorphisms and subdirect products of free contents (unpublished).
  • [9] Takayuki Tamura, Commutative nonpotent archimedean semigroup with cancelation law. I., J. Gakugei Tokushima Univ. 8 (1957), 5–11. MR 0096741
  • [10] -, 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.

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Keywords: Matrix of commutative cancellative semigroups, Rees matrix semigroup, quotient Rees matrix semigroup, quotient group
Article copyright: © Copyright 1975 American Mathematical Society

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