Decomposition of primes in non-maximal orders
نویسندگان
چکیده
منابع مشابه
Maximal Orders in Semigroups1
Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0-simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of group of quotients [8]. To give the definition we first have to explain what is meant by a squar...
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These notes are an attempt to unify the presentations of associated primes and primary decomposition given by Atiyah-Macdonald [1], Bourbaki [2], and Matsumura [3]. Their definitions differ somewhat, and we hope that the ways in which we have chosen to highlight these differences will lead to the reader having a greater understanding of the important concepts described herein. The differing def...
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If N is a submodule of the R-module M , and a ∈ R, let λa : M/N → M/N be multiplication by a. We say that N is a primary submodule of M if N is proper and for every a, λa is either injective or nilpotent. Injectivity means that for all x ∈ M , we have ax ∈ N ⇒ x ∈ N . Nilpotence means that for some positive integer n, aM ⊆ N , that is, a belongs to the annihilator of M/N , denoted by ann(M/N). ...
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The free monoid, or the set of words on an alphabet, can be made into a poset (patially ordered set) by different kind of orders, one example in view is the lexicographic arrangement of words in a dictionary. One can also order the words by their length: the shorter words precede the longer ones in this order. The structure of an odered set is usually determined by its chains in the one hand an...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2005
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa120-3-2