A NOTE ON THE CANCELLATION PROPERTIES OF SEMISTAR OPERATIONS

Authors : S T Chapman, Ryûki Matsuda

Pages : 78-86

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Publication Date : 2010-06-01

Article Type : Research Paper

Abstract :If D is an integral domain with quotient field K, then let Finsert ignore into journalissuearticles values( ¯ D); be the set of non-zero D-submodules of K, Finsert ignore into journalissuearticles values(D); be the set of non-zero fractional ideals of D and finsert ignore into journalissuearticles values(D); be the set of non-zero finitely generated D-submodules of K. A semistar operation ? on D is called arithmetisch brauchbar insert ignore into journalissuearticles values(or a.b.); if, for every H ∈ finsert ignore into journalissuearticles values(D); and every H1, H2 ∈ Finsert ignore into journalissuearticles values( ¯ D);, insert ignore into journalissuearticles values(HH1);? = insert ignore into journalissuearticles values(HH2);? implies H?1 = H?2, and ? is called endlich arithmetisch brauchbar insert ignore into journalissuearticles values(or e.a.b.); if the same holds for every F, F1, F2 ∈ finsert ignore into journalissuearticles values(D);. In this note, we introduce the notion of strongly arithmetisch brauchbar insert ignore into journalissuearticles values(or s.a.b.); and consider relationships among semistar operations suggested by other related cancellation properties.
Keywords : semistar operation