منابع مشابه
When Is the Semigroup Ring Perfect?
A characterization of perfect semigroup rings A[G] is given by means of the properties of the ring A and the semigroup G. It was proved in [10] that for a ring with unity A and a group G the group ring A[G] is perfect if and only if A is perfect and G is finite. Some results on perfectness of semigroup rings were obtained by Domanov [3]. He reduced the problem of describing perfect semigroup ri...
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Let $M(X, mathcal{A}, mu)$ be the ring of real-valued measurable functions on a measure space $(X, mathcal{A}, mu)$. In this paper, we characterize the maximal ideals in the rings of real measurable functions and as a consequence, we determine when $M(X, mathcal{A}, mu)$ is a hereditary ring.
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The topology of a conjugated molecule plays a significant role in controlling both the electronic properties and the conformational manifold that the molecule may explore. Fully π-conjugated molecular nanorings are of particular interest, as their lowest electronic transition may be strongly suppressed as a result of symmetry constraints. In contrast, the simple Kasha model predicts an enhancem...
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Life on earth has evolved on a photic carousel, spinning through alternating periods of light and darkness. This playful image belies the fact that only those organisms that learned how to benefit from the recurring features in their environment were allowed to ride on. This selection process has engendered many daily rhythms in our biosphere, most of which rely on the anticipatory power of an ...
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This is an expanded version of a series of four lectures designed to show algebraists how ring theoretical methods can be used to analyze an interesting family of finite Markov chains. The chains happen to be random walks on semigroups, and the analysis is based on a study of the associated semigroup algebras. The paper is divided into four sections, which correspond roughly to the four lecture...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0706509-5