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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Algebra universalis 36 (1996), S. 392-404 
    ISSN: 1420-8911
    Keywords: 06F10 ; 06F99 ; 13A15 ; multiplicative lattices ; Noether lattice ; principal element
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Principal elements were introduced in multiplicative lattices by R. P. Dilworth, following an earlier but less successful attempt in the joint work of Ward and Dilworth. As suggested by their name, principal elements are the analogue in multiplicative lattices of principal ideals in (commutative) rings. Principal elements are the cornerstone on which the theory of multiplicative lattices and abstract ideal theory now largely rests. In this paper, we obtain some new results regarding principal elements and extend some others. In addition, we try to convey what is known and what is not known about the subject. We conclude with a fairly extensive (but likely not exhaustive) bibliography on principal elements.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2242
    Keywords: Phaseolus vulgaris L Uromyces appendiculatus ; Gene pyramiding Near-isogenic lines (NILs) ; Genetic markers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The Guatemalan black bean (Phaseolus vulgaris L.) plant introduction (PI) 181996 is resistant to all known US races of the bean rust fungus Uromyces appendiculatus (Pers. ex Pers.) Unger var. appendiculatus [syn. U. phaseoli (Reben) Wint.]. We report on two random amplified polymorphic DNA (RAPD) markers OAC20490 tightly linked (no recombinants) in coupling phase and OAE19890 linked in repulsion phase (at 6.2±2.8 cM) to PI 181996 rust resistance. These RAPDs, generated by single decamer primers in the polymerase chain reaction, were identified in near-isogenic bulks of non-segregating resistant and susceptible BC4F2 (NX-040*4/PI 181996) lines. Linkage of the RAPD markers was confirmed by screening 19 BC4F2 and 57 BC4F3 individuals segregating for PI 181996 resistance. Utility of the RAPDs OAC20490 and OAE19890 was investigated in a diverse group of common bean cultivars and lines. All cultivars into which the PI 181996 resistance was introgressed had the RAPD OAC20490. A RAPD similar in size to OAC20490, observed in some susceptible common bean lines, was confirmed by Southern blotting to be homologous to the RAPD OAC20490. Use of the RAPDs OAC20490 and OAE19890 in marker-assisted selection (MAS) is proposed. The coupling-phase RAPD is most useful for MAS of resistant BCnF1individuals during traditional backcross breeding. The repulsion-phase RAPD has greatest utility in MAS of homozygous-resistant individuals in F2 or later-segregating generations.
    Type of Medium: Electronic Resource
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