Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Commutative Semigroups whose Proper Homomorphic Images are All of Smaller Cardinality

  • Tucci, Ralph P. (Department of Mathematics and Computer Science, Loyola University New Orleans)
  • Received : 2004.11.05
  • Published : 2006.06.23
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Abstract

We characterize those commutative semigroups S such that every non-isomorphic homomorphic image of S has smaller cardinality than S. We also characterize commutative groups with the same property.

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References

  1. A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Amer. Math. Soc., Providence, Rhode Island, 1(1961).
  2. B. A. Jensen and D. W. Miller, Commutative Semigroups Which Are Almost Finite, Pacific J. Math., 27(1968), 533-538. https://doi.org/10.2140/pjm.1968.27.533
  3. I. Kaplansky, Infinite Abelian Groups, The University of Michigan Press, Ann Arbor, Michigan, 1954.