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Prime ideals in autometrized algebras. (English) Zbl 0692.06007
The author introduces the notion of a prime ideal in an autometrized algebra and obtains certain natural consequences of the definition in semiregular normal autometrized algebras. Almost all the results of this paper have been obtained for seminormal and semiregular autometrized algebra by N. Prabhakara Rao in his Ph. D. Thesis [“On certain classes of autometrized algebras”, Section 1.3, Andhra Univ., Waltair (1977)].

MSC:
06F05 Ordered semigroups and monoids
20M14 Commutative semigroups
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References:
[1] K. L. N. Swamy: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105-114. · Zbl 0138.02104 · doi:10.1007/BF01364335 · eudml:161279
[2] K. L. N. Swamy N. P. Rao: Ideals in autometrized algebras. J. Austral. Math. Soc. (Ser. A) 24 (1977), 362-374. · Zbl 0427.06006 · doi:10.1017/S1446788700020383
[3] K. L. N. Swamy B. V. Subba Rao: Isometries in dually residuated lattice ordered semigroups. Math. Sem. Notes 8 (1980), 369-380. · Zbl 0464.06008
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