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Indecomposable baric algebras. II. (English) Zbl 0811.17035
The concept and properties of indecomposability for baric algebras having an idempotent of weight one were introduced in the review of Part I above [same journal 183, 223-236 (1993; Zbl 0811.17034)].
First, a sufficient condition to ensure that the commutative duplicate of a commutative indecomposable baric algebra is indecomposable, is established by the authors. Then, the notion of closed class is defined, and several theorems, giving examples of closed classes, are proved. In the last part, the gametic and zygotic algebras for $$k$$ linked or independent loci are proved to be indecomposable.

##### MSC:
 17D92 Genetic algebras 92D10 Genetics and epigenetics
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##### References:
 [1] Costa, R.; Guzzo, H., Indecomposable baric algebras, Linear algebra appl., 183, 223-236, (1993) · Zbl 0811.17034 [2] Heuch, I., Genetic algebras for systems with linked loci, Math. biosci., 34, 35-47, (1977) · Zbl 0361.92015 [3] Holgate, Ph., The gametic algebra of k linked loci, Proc. London math. soc., 18, 3, 315-327, (1968) · Zbl 0157.26703 [4] Holgate, Ph., Canonical multiplication in the genetic algebra for linked loci, Linear algebra appl., 26, 281-287, (1979) · Zbl 0408.92004 [5] Mallol, C.; Micali, A., Sur LES algèbres de Bernstein. IV, Linear algebra appl., 158, 1-26, (1991) · Zbl 0742.17029 [6] Osborn, J.M., Varieties of algebras, Adv. in math., 8, 163-369, (1972) · Zbl 0232.17001 [7] Wörz, A., Algebras in genetics, () · Zbl 0431.92017
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