Journal article
Multiplicative lattices in which every principal element is a product of prime elements
Algebra universalis., Vol.8, pp.330-335
1978
DOI: 10.1007/BF02485403
Abstract
In this paper we study multiplicative lattices with the property that every principal element is a product of prime elements. This paper is a continuation of Section 4 of [2]; however, here we restrict ourselves to r-lattices.
An r-lattice L is called a 7r-lattice if there exists a set S of elements of L (not necessarily principal) which generate L under joins such that every element of S is a finite product of prime elements. We call a 7r-lattice without divisors of zero a "rr-lattice domain.
In Theorem 4.2 [2] we showed that a quasi-local 7r-lattice is either a domain or a very special type of Noether lattice which we will call a special 7r-lattice. A special 7r-lattice is a local Noether lattice satisfying (1) every rank zero prime element is principal and (2) every principal element is a product of rank zero primes. A special 7r-lattice with exactly one minimal prime element is called a
special principal element lattice.
Details
- Title: Subtitle
- Multiplicative lattices in which every principal element is a product of prime elements
- Creators
- D.D. Anderson - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Algebra universalis., Vol.8, pp.330-335
- Publisher
- Birkhäuser-Verlag
- DOI
- 10.1007/BF02485403
- ISSN
- 0002-5240
- eISSN
- 1420-8911
- Comment
- References: Anderson, D.D., Distributive Noether lattices (1975) The Michigan Mathematical Journal, 22, pp. 109-115; Anderson, D.D., Abstract commutative ideal theory without chain condition (1976) Algebra Universalis, 6, pp. 131-145; Anderson, D.D., Matijevic, J., Nichols, W., The Intersection Theorem. II (1976) Pacific Journal of Mathematics, 66, pp. 15-22; Bogart, K.P., Structure theorems for regular Noether lattices (1968) The Michigan Mathematical Journal, 15, pp. 167-176; Bogart, K.P., Distributive local Noether lattices (1969) The Michigan Mathematical Journal, 16, pp. 215-223; Bogart, K.P., Small regular local Noether lattices. I (1970) Proceedings of the American Mathematical Society, 25, pp. 423-428; Gilmer, R., (1972) Multiplicative ideal theory, , Marcel Dekker, New York; Johnson, E.W., Lediaev, J.P., Representable distributive Noether lattices (1969) Pacific Journal of Mathematics, 28, pp. 561-564
- Language
- English
- Date published
- 1978
- Academic Unit
- Mathematics
- Record Identifier
- 9984230625802771
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