Perspectivity and cancellation in regular rings
نویسندگان
چکیده
منابع مشابه
Commuting $pi$-regular rings
R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.
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In this paper, we study the class of rings that satisfy internal direct sum cancellation with respect to their 1-sided ideals. These are known to be precisely the rings in which regular elements are unitregular. Further characterizations for such “IC rings” are given, in terms of suitable versions of stable range conditions, and unique generator properties of idempotent generated right ideals. ...
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A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1977
ISSN: 0021-8693
DOI: 10.1016/0021-8693(77)90289-7