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Cornish, W. H.; Stewart, P. N.

Direct and subdirect decompositions of universal algebras with a Boolean orthogonality. (English) Zbl 0482.08001

Acta Math. Acad. Sci. Hung. 38, 9-14 (1981).
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Cited in 2 Documents

MSC:

08A05 Structure theory of algebraic structures
08A30 Subalgebras, congruence relations
06B10 Lattice ideals, congruence relations

Keywords:

subdirect decompositions of universal algebras; Boolean orthogonality; polars; orthodirect decomposition; orthosubdirect decompositions; congruence relations; prime ideals

Citations:

Zbl 0375.06002
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Full Text: DOI

References:

[1] A. Abian, Direct product decomposition of commutative semi-simple rings,Proc. Amer. Math. Soc.,24 (1970), 502–507. · Zbl 0207.05002
[2] D. H. Adams, Semigroups with no non-zero nilpotent elements.Math. Z.,123 (1971), 168–176. · Zbl 0212.35803 · doi:10.1007/BF01110115
[3] M. Chacron, Direct products of division rings and a paper of Abian,Proc. Amer. Math. Soc.,29 (1971), 259–262. · Zbl 0251.16014 · doi:10.1090/S0002-9939-1971-0274512-X
[4] W. H. Cornish, Subdirectly irreducible semirings and semigroups without non-zero nilpotents,Canad. Math. Bull.,16 (1973), 45–47. · Zbl 0271.16021 · doi:10.4153/CMB-1973-010-4
[5] W. H. Cornish, Boolean orthogonalities and minimal prime ideals,Communications in Algebra,3 (1975), 859–900. · Zbl 0375.06002 · doi:10.1080/00927877508822078
[6] W. H. Cornish andP. N. Stewart, Wealky regular algebras, Boolean orthogonalities and direct products of integral domains,Can. J. Math.,28 (1976), 148–153. · Zbl 0302.16016 · doi:10.4153/CJM-1976-018-7
[7] G. Davis, Rings with orthogonality relations,Bull. Austral. Math. Soc.,4 (1971), 163–178. · Zbl 0203.33901 · doi:10.1017/S0004972700046426
[8] G. Grätzer, Universal Algebra,Van Nostrand (Princeton 1968).
[9] I. R. Hentzel, Alternative rings without nilpotent elements,Proc. Amer. Math. Soc.,42 (1974), 373–376. · Zbl 0253.17018 · doi:10.1090/S0002-9939-1974-0327858-3
[10] L. Levy, Unique subdirect sums of prime rings,Trans. Amer. Math. Soc.,106 (1963), 64–76. · Zbl 0113.25903 · doi:10.1090/S0002-9947-1963-0142567-9
[11] H. C. Myung andL. R. Jimenez, Direct product decomposition of alternative rings,Proc. Amer. Math. Soc.,47 (1975), 53–60. · Zbl 0301.17004 · doi:10.1090/S0002-9939-1975-0354796-3
[12] R. S. Pierce,Introduction to the Theory of Abstract Algebras (Holt, Rinehart and Winston (New York, 1968).
[13] Ju. M. Rjabuhin, Algebras without nilpotents II,Algebra and Logic,8 (1969), 123–137. · doi:10.1007/BF02219832
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