Abstract
By using the concept of modular commutator, prime congruences are defined for algebras in modular varieties. Then the prime spectrum of an algebra is defined and various spectral properties are discussed. In particular some conditions are given for the spectrum of an algebra to be homeomorphic to a ring spectrum.
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References
Agliano, P.,The prime spectrum of a universal algebra, Rivista di Mat. Pura ed Appl4 (1989), 83–91.
Agliano, P. andUrsini, A.,On some Ideal Basis Theorems, submitted to Algebra Universalis.
Comer, S.,A sheaf-theoretic duality theorem for cylindrical algebras, Trans. Am. Math. Soc.169 (1972), 75–87.
Fichtner, K.,Eine Bemerkung über Mannigfaltigkeiten Universeller Algebren, Monatsch. d. Deutsch. Akad. d. Wiss. (Berlin)12 (1979), 21–45.
Freese, R. andMcKenzie, R.,Commutator Theory for Congruence Modular Varieties, London Math. Soc. Lecture Note Series, Cambridge University Press, Cambridge, 1987.
Gumm, H. P. andUrsini, A.,Ideals in Universal Algebra, Algebra Universalis19 (1984), 45–54.
Hochster, M.,Prime ideal structure in commutative rings, Trans. Am. Math. Soc.127 (1969), 43–60.
Kollar, J.,Congruence and one element subalgebras, Algebra Universalis9 (1979), 266–267.
Lambek, J. andMoerdijk, I,Two sheaf representations in elementary toposes, inThe L.E.J. Brouwer centenary symposium, North Holland, 1982, pp. 275–292.
Schmidt, E. T.,The ideal lattice of a distributive lattice with 0is the congruence lattice of a lattice, Acta Sci. Math. (Szeged)43 (1981), 153–168.
Ursini, A.,Sulle varietá di algebre con una buona teoria degli ideali, Boll. U.M.I.6 (1972), 90–95.
Wolf, A.,Sheaf representations of arithmetical algebras, inRecent advances in the representation theory of rings and C *-algebras, Memoirs Amer. Math. Soc.148 (1974), 87–93.