منابع مشابه
Local and global tameness in Krull monoids
Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t(H) equals zero if and only if H is factorial (equivalently, |G| = 1). If |G| > 1, then D(G) ≤ t(H) ≤ 1 + D(G) (
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Let M be a Krull monoid. Then every element of M may be written as a finite product of irreducible elements. If for every a ∈ M , each two factorizations of a have the same number of irreducible elements, then M is called half-factorial. Using a property of element exponentiation, we provide a new characterization of half-factoriality, valid for all Krull monoids whose class group has torsion-f...
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Let M be a commutative cancellative monoid. The set ∆(M), which consists of all positive integers which are distances between consecutive irreducible factorization lengths of elements in M , is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with divisor class group Zn, then it is well-known that ∆(M) ⊆ {1, 2, . . . , n − 2}. Moreover, equality holds fo...
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The Catalan monoid and partial Catalan monoid of a directed graph are introduced. Also introduced is the notion of a local endomorphism of a tree, and it is shown that the Catalan (resp. partial Catalan) monoid of a tree is simply its monoid of extensive local endomorphisms (resp. partial endomorphisms) of nite shift. The main results of this paper are presentations for the Cata-lan and partial...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2014
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2014.897585