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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Principal ideals in the ideal lattice

Author: H. Subramanian
Journal: Proc. Amer. Math. Soc. 31 (1972), 445
MathSciNet review: 0284424
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Abstract | References | Additional Information

Abstract: We show that there cannot be a definition of ``principal elements'' in the theory of multiplicative lattices so that the notion of principal elements concurs with the notion of principal ideals when interpreted in the ideal lattices of rings.

References [Enhancements On Off] (What's this?)

  • [1] R. P. Dilworth, Abstract commutative ideal theory, Pacific J. Math. 12 (1962), 481-498. MR 26 #1333. MR 0143781 (26:1333)
  • [2] H. Subramanian, On theory of $ x$-ideals, J. Algebra 12 (1969), 134-142. MR 39 #1385. MR 0240031 (39:1385)

Additional Information

Keywords: Dedekind ring, ideal lattice, principal ideal, $ m$-lattice
Article copyright: © Copyright 1972 American Mathematical Society

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