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ABSTRACT
<u>Introducstion</u>. Although most of the applications of computers to abstract algebra have been made in group theory [4], there have been several applications to finite semigroups and related structures. Most of the work in this area has been concentrated on enumerative type problems and backtrack methods [11] in searching for examples of specific types of structures. Recently however, several papers have appeared that describe computer applications to the analyzation of specific structures and to the investigation of word problems in semigroups.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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1
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M. Anshel and J. R. Clay, "Planar Algebraic Systems: Some Geometric Interpretations", J. Algebra 10 (1968), 166--173.
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2
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R. C. Buck, "On Certain Decidable Semigroups", to appear.
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3
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R. C. Buck, "Decidable Semigroups", to appear.
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4
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5
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J. R. Clay, "The Near-rings on Groups of Low Order", Math. Z. 104 (1968), 364--371.
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6
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J. R. Clay, "Research in Near-ring Theory Using a Digital Computer", to appear.
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7
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T. Evans, "Products of Points - Some Simple Algebras and Their Identities", Amer. Math. Monthly 74 (1967), 362--372.
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8
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G. E. Forsythe, "SWAC Computes 126 Distinct Semigroups of Order 4", Proc. Amer. Math. Soc. 6 (1955), 443--447.
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9
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M. Hall and D. E. Knuth, "Combinatorial Analysis and Computers", Amer. Math. Monthly 72 (1965), Part II, 21--28.
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10
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D. E. Knuth and P. B. Bendix, "Simple Word Problems in Universal Algebras", pp. 263--297 in: J. Leech, "Computational Problems in Abstract Algebra", Pergamon Press, Oxford, 1969.
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11
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D. H. Lehmer, "Teaching Combinatorial Tricks to a Computer", A. M. S. Proc. of Symposia in Appl. Math. 10 (1960), 179--193.
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12
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M. Petrich, "Associative Polynomial Multiplication Over an Infinite Integral Domain", Math. Nachr. 29 (1965), 67--75.
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13
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R. J. Plemmons, "Cayley Tables for all Semigroups of Order N ≤ 6", Monograph, Auburn University, 1966.
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14
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R. J. Plemmons, "Construction and Analysis of Non-equivalent Finite Semigroups", pp. 223--228 in: J. Leech, "Computational Problems in Abstract Algebra", Pergamon Press, Oxford, 1969.
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15
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R. J. Plemmons and M. T. West, "On the Semigroup of Binary Relations", submitted to J. London Math. Soc.
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16
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R. J. Plemmons and M. T. West, "Maximal Subgroups of the Semigroup of Relations", submitted to J. Algebra.
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17
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R. J. Plemmons and R. Yoshida, "Generating Polynomials for Finite Semigroups", J. Austral. Math. Soc., to appear.
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18
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S. Schwarz, "The Semigroups of Binary Relations on a Finite Set", Czechoslovak Math. J., to appear.
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19
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T. Tamura, "Some Remarks on Semigroups of all Types of Order 2, 3", J. Gakugei Tokushima Univ. 3 (1953), 1--11.
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20
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T. Tamura, M. Nakao, M. Shingai, Y. Iwano, K. Minami, K. Nii and H. Tateyama, "Distributive Multiplications to Semigroup Operations", J. Gakugei Tokushima Univ. 8 (1957), 91--101; errata 9 (1958), 25.
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21
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K. Tetsuya, T. Hashimoto, T. Akazawa, R. Shibata, T. Inui and T. Tamura, "All Semigroups of Order at Most 5", J. Gakugei Tokushima Univ. 6 (1955), 19--39.
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22
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M. T. West, "On the Semigroup of Binary Relations on a Set", M. A. Thesis, Univ. of Tennessee, 1968.
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23
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R. Yoshida, "On Some Semigroups", Bull. Amer. Math. Soc. 69 (1963), 369--371.
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24
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R. Yoshida, "Remarks on Finite Commutative Z-Semigroups", Mem. Res. Inst. of Ritumeikan Univ. 16 (1967), 1--11.
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