کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4585275 1630526 2013 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Exact rings and semirings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Exact rings and semirings
چکیده انگلیسی

We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn–Banach-type separation property on modules. Our motivation comes from the tropical semiring, and in particular a desire to understand the often surprising extent to which it behaves like a field. The definition of exactness abstracts an elementary property common to both fields and the tropical semiring, which we believe is fundamental to explaining this similarity. The class of exact semirings turns out to include many other important examples of both rings (proper quotients of principal ideal domains, matrix rings and finite group rings over these and over fields), and semirings (the Boolean semiring, generalisations of the tropical semiring, matrix semirings and group semirings over these).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 388, 15 August 2013, Pages 324–337
نویسندگان
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