منابع مشابه
Strongly Rational Comodules and Semiperfect Hopf Algebras over QF Rings
Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right Ccomodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over...
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modulo the condition that ' (a) = a for all a 2 A if P holds. If ' is the injection map A B, then C is simply the union A [ fb 2 B : Pg, which is a subring of B. This is the case of most interest when dealing with discrete rings. Interpolated rings are used to construct Brouwerian examples. For example, the interpolated rings in Z Q provide a Brouwerian example of a discrete ring C and a nitel...
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. . l 'be&t imd~in i te~ard~en~th (FWL) state-space digital comp&satordesign~r~b lem is investigated. Instead of the usual sensitivity measure, it h argued that it may be desirable to mini&e a frequency weighted sensitivity measure over all similarity bmformations. The set of optimal realizations minimizing this weighted sensitivity b completely chaacterized, and an algorithm is proposed to fin...
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Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1) y]=[[x ,_( n) y] , y]. In this paper we show that necessary and sufficient conditions for RG to satisfies [x^m(x,y) ,_( n(x,y)) y]=0 is: 1) if r is a power of a prime p, then G is a locally nilpotent group an...
متن کاملA note on the socle of certain types of f-rings
For any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. The condition is that every minimal ideal of the ring consist entirely of bounded elements. It is not too stringent, and is satisfied, for instance, by rings of ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1973
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1973.44.309