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Irreducibility of ideals in a one-dimensional analytically irreducible ring

Valentina Barucci, Faten Khouja (2010)

Actes des rencontres du CIRM

Let R be a one-dimensional analytically irreducible ring and let I be an integral ideal of R . We study the relation between the irreducibility of the ideal I in R and the irreducibility of the corresponding semigroup ideal v ( I ) . It turns out that if v ( I ) is irreducible, then I is irreducible, but the converse does not hold in general. We collect some known results taken from [5], [4], [3] to obtain this result, which is new. We finally give an algorithm to compute the components of an irredundant decomposition...

Isotopy invariant quasigroup identities

Aleksandar Krapež, Bojan Marinković (2016)

Commentationes Mathematicae Universitatis Carolinae

According to S. Krstić, there are only four quadratic varieties which are closed under isotopy. We give a simple procedure generating quadratic identities and deciding which of the four varieties they define. There are about 37000 such identities with up to five variables.

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