Geodesic
On reductive and distributive algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 617-629 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper investigates idempotent, reductive, and distributive groupoids, and more generally $\Omega$-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left $k$-step reductive $\Omega$-algebras, and of right $n$-step reductive $\Omega$-algebras, are independent for any positive integers $k$ and $n$. This gives a structural description of algebras in the join of these two varieties.
The paper investigates idempotent, reductive, and distributive groupoids, and more generally $\Omega$-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left $k$-step reductive $\Omega$-algebras, and of right $n$-step reductive $\Omega$-algebras, are independent for any positive integers $k$ and $n$. This gives a structural description of algebras in the join of these two varieties.
Classification : 03C05, 08A05, 08B05, 08C15
Keywords: idempotent and distributive groupoids and algebras; Mal'cev products of varieties of algebras; independent varieties 
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     author = {Romanowska, Anna},
     title = {On reductive and distributive algebras},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {617--629},
     year = {1999},
     volume = {40},
     number = {4},
     mrnumber = {1756540},
     zbl = {1010.08002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_4_a1/}
}
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Romanowska, Anna. On reductive and distributive algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 617-629. http://geodesic.mathdoc.fr/item/CMUC_1999_40_4_a1/