کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4583696 1630451 2016 47 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Idempotent plethories
ترجمه فارسی عنوان
بازیهای مشابه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let k be a commutative ring with identity. A k-plethory is a commutative k-algebra P   together with a comonad structure WPWP, called the P-Witt ring functor, on the covariant functor that it represents. We say that a k-plethory P is idempotent   if the comonad WPWP is idempotent, or equivalently if the map from the trivial k  -plethory k[e]k[e] to P is a k-plethory epimorphism. We prove several results on idempotent plethories. We also study the k  -plethories contained in K[e]K[e], where K is the total quotient ring of k  , which are necessarily idempotent and contained in Int(k)={f∈K[e]:f(k)⊆k}Int(k)={f∈K[e]:f(k)⊆k}. For example, for any ring l between k and K we find necessary and sufficient conditions—all of which hold if k   is a integral domain of Krull type—so that the ring Intl(k)=Int(k)∩l[e]Intl(k)=Int(k)∩l[e] has the structure, necessarily unique and idempotent, of a k  -plethory with unit given by the inclusion k[e]⟶Intl(k)k[e]⟶Intl(k). Our results, when applied to the binomial plethory Int(Z)Int(Z), specialize to known results on binomial rings.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 463, 1 October 2016, Pages 33–79
نویسندگان
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