CANCELLATION PROPERTIES IN IDEAL SYSTEMS OF MONOIDS

Authors : Ryûki Matsuda

Pages : 61-68

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Publication Date : 2011-06-01

Article Type : Research Paper

Abstract :We pursue the work by M. Fontana, K.A. Loper and R. Matsuda. Let D be an integral domain, let Finsert ignore into journalissuearticles values(D); insert ignore into journalissuearticles values(resp., finsert ignore into journalissuearticles values(D);); be the set of non-zero insert ignore into journalissuearticles values(resp., finitely generated); fractional ideals of D, let ? be a semistar operation on D. They showed that if ? satisfies insert ignore into journalissuearticles values(F F1);? = insert ignore into journalissuearticles values(F F2);? implies F?1 = F?2 for every F, F1, F2 ∈ finsert ignore into journalissuearticles values(D);, then ? need not satisfy insert ignore into journalissuearticles values(F G1);? = insert ignore into journalissuearticles values(F G2);? implies G?1 = G?2 for every F ∈ finsert ignore into journalissuearticles values(D); and every G1, G2 ∈ Finsert ignore into journalissuearticles values(D);. In this paper, we show its analogy for monoids.
Keywords : semistar operation, monoid