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( δ , 2 ) -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

Let R be a commutative ring with nonzero identity, let ( ) be the set of all ideals of R and δ : ( ) ( ) an expansion of ideals of R defined by I δ ( I ) . We introduce the concept of ( δ , 2 ) -primary ideals in commutative rings. A proper ideal I of R is called a ( δ , 2 ) -primary ideal if whenever a , b R and a b I , then a 2 I or b 2 δ ( I ) . Our purpose is to extend the concept of 2 -ideals to ( δ , 2 ) -primary ideals of commutative rings. Then we investigate the basic properties of ( δ , 2 ) -primary ideals and also discuss the relations among ( δ , 2 ) -primary, δ -primary and...

A Characterization of Multidimensional S -Automatic Sequences

Emilie Charlier, Tomi Kärki, Michel Rigo (2009)

Actes des rencontres du CIRM

An infinite word is S -automatic if, for all n 0 , its ( n + 1 ) st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S . In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d 2 , we state that a multidimensional infinite word x : d Σ over a finite alphabet Σ is S -automatic for some abstract numeration...

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