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On semisubtractive halfrings

Published online by Cambridge University Press:  17 April 2009

R.E. Dover  and
H.E. Stone
R.E. Dover
Affiliation:
Department of Mathematics, Lubbock Christian College, Lubbock, Texas, USA.
H.E. Stone
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.
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Abstract

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Analogues of Artin-Wedderburn and Goldie structure theorems are obtained for a class of halfrings which includes the semisubtractive ones. In the semisubtractive case, precise results are obtained which show that non-ring examples of these structures are relatively limited.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 371 - 378
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Dover, Ronald Eugene, “Semisimple semirings”, (Doctoral Dissertation, Texas Christian University, Forth Worth, 1972).Google Scholar
[2]Dulin, Bill J. and Mosher, James R., “The Dedekind property for semirings”, J. Austral. Math. Soc. 14 (1972), 82–90.CrossRefGoogle Scholar
[3]Mosher, James R., “Generalized quotients of hemirings”, Compositio Math. 22 (1970), 275–281.Google Scholar
[4]Mosher, James R., “Semirings with descending chain condition and without nilpotent elements”, Compositio Math. 23 (1971), 79–85.Google Scholar
[5]Smith, David A., “On semigroups, semirings, and rings of quotients”, J. Sci. Hiroshima Univ. Ser. A-I Math. 30 (1966), 123–130.Google Scholar
[6]Smith, F.A., “A structure theory for a class of lattice ordered semirings”, Fund. Math. 59 (1966), 49–64.CrossRefGoogle Scholar
[7]Smith, F.A., “A subdirect decomposition of additively idempotent semirings”, J. Natur. Sci. and Math. 7 (1967), 253–257.Google Scholar
[8]Smith, F.A., “l–semirings”, J. Natur. Sci. and Math. 8 (1968), 95–98.Google Scholar
[9]Stone, H.E., “Ideals in haifrings”, Proc. Amer. Math. Soc. 33 (1972), 8–14.CrossRefGoogle Scholar
[10]Wiegandt, Richard, “Über die Struktursätze der Halbringe”, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 5 (1962), 51–68.Google Scholar