1404/04/20
سعید باقری (بازنشسته)

سعید باقری (بازنشسته)

مرتبه علمی: استادیار
ارکید:
تحصیلات: دکترای تخصصی
اسکاپوس:
دانشکده: دانشکده علوم ریاضی و آمار
نشانی: ملایر-کیلومتر 4 جاده اراک-دانشگاه ملایر- دانشکده علوم ریاضی- گروه ریاضی
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مشخصات پژوهش

عنوان
SEMISIMPLE DIMENSION OF MODULES
نوع پژوهش
JournalPaper
کلیدواژه‌ها
uniform dimension, semisimple module, artinian module.
سال
2018
مجله Communications of the Korean Mathematical Society
شناسه DOI
پژوهشگران Saeid Bagheri

چکیده

In this paper we de ne and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. We give some interesting and useful properties of rings or modules which have semisimple dimension. It is shown that a noetherian module with semisimple dimension is an artinian module. A domain with semisimple dimension is a division ring. Also, for a semiprime right non-singular ring R, if its maximal right quotient ring has semisimple dimension as a right R-module, then R is a semisimple artinian ring. We also characterize rings whose modules have semisimple dimension. In fact, it is shown that all right R-modules have semisimple dimension if and only if the free right R-module \sum 1 to Inf=1R has semisimple dimension, if and only if R is a semisimple artinian ring.