rings in which elements are the sum of an idempotent and a regular element
نویسندگان
چکیده
let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents in r, then an r-clean ring is an exchange ring. also we show that the center of an r-clean ring is not necessary r-clean, but if 0 and 1 are the only idempotents in r, then the center of an r-clean ring is r-clean. finally we give some properties and examples of r-clean rings
منابع مشابه
Rings in which elements are the sum of an idempotent and a regular element
Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents...
متن کاملrings in which elements are the sum of an idempotent and a regular element
let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...
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it is not possible to understand developments of a country’s culture and civilization without knowing his believes and myths. whether it is north or south, east or west, planes or mountains, sahara or deserts, here in iran every corner includes valuable and precious treasures which are known all over the world, and cultural – historical objects which are found here adorn all well known museums...
a study of the fifth child and ben in the world by doris lessing in the light of julia kristevas psychoanalytic concepts
این مطالعه به بررسی عوامل روانشناختی کریستوادردو رمان دوربس لسینگ،فرزندبنجم و بن دردنیای واقعی می بردازد.موفقیت یا شکست کاراکترهادر تکمیل شکست تتیزی یه کمک بدر وهم از مهم ترین دغدغه محقق می باشد.به بررسی تحلیل روانشناختی تمامی کاراکترها خصوصا بن برداخته و به دنبال نشانه هایی از جامعه شیشه ای کریستوا می باشد.
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bulletin of the iranian mathematical societyجلد ۳۹، شماره ۳، صفحات ۵۷۹-۵۸۸
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