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1.
LetF be an algebraically closed field. A be a finite-dimensional algebra overF A be the Auslander-Reiten quiver ofA,Γ be a connected component of Γ A with oriented cycles and semi-stable vertices and each non-stable vertex In Γ be a projective-injective vertex. The structure of Γ is studied. Projcct supported by Chinese Postdoctor Fund.  相似文献
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In this paper, we introduce the notion of (*)-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of (*)-serial coalgebras and their comodules, and obtain sufficient and necessary conditions for a basic coalgebra to be (*)-serial.  相似文献
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Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain sufficient and necessary conditions for an associative algebra to be (*)-serial.  相似文献
5.
Wei Meng  Hailou Yao  Li Ma 《代数通讯》2018,46(3):1252-1258
Let G be a finite group and δ(G) denote the number of conjugacy classes of all non-cyclic subgroups of G. The symbol π(G) denotes the set of the prime divisors of |G|. In [7 Meng, W., Li, S. R. (2014). Finite groups with few conjugacy classes of non-cyclic subgroups. Scientia Sin. Math. 44:939944.[Crossref] [Google Scholar]], Meng and Li showed the inequality δ(G)≥2|π(G)|−2, where G is non-cyclic solvable group. In this paper, we describe the finite groups G such that δ(G) = 2|π(G)|−2. Another aim of this paper would show δ(G)≥M(G)+2 for unsolvable groups G and the equality holds ⇔GA5 or SL(2,5), where M(G) denotes the number of conjugacy classes of all maximal subgroups of G.  相似文献
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Let \(\mathcal{N}\) denote the class of nilpotent Lie algebras. For any finite-dimensional Lie algebra L over an arbitrary field \(\mathbb{F}\), there exists a smallest ideal I of L such that L/I\(\mathcal{N}\). This uniquely determined ideal of L is called the nilpotent residual of L and is denoted by L\(\mathcal{N}\). In this paper, we define the subalgebra S(L) = ∩HLIL(H\(\mathcal{N}\)). Set S0(L) = 0. Define Si+1(L)/Si(L) = S(L/Si(L)) for i > 1. By S(L) denote the terminal term of the ascending series. It is proved that L = S(L) if and only if L\(\mathcal{N}\) is nilpotent. In addition, we investigate the basic properties of a Lie algebra L with S(L) = L.  相似文献
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Let G be a finite group and NA(G) denote the number of conjugacy classes of all nonabelian subgroups of non-prime-power order of G. The Symbol π(G) denote the set of the prime divisors of |G|. In this paper we establish lower bounds on NA(G). In fact, we show that if G is a finite solvable group, then NA(G) = 0 or NA(G) ≥ 2|π(G)|−2, and if G is non-solvable, then NA(G) ≥ |π(G)| + 1. Both lower bounds are best possible.  相似文献
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We investigate the comodule representation category over the Morita-Takeuchi context coalgebra Γ and study the Gorensteinness of Γ. Moreover, we determine explicitly all Gorenstein injective comodules over the Morita-Takeuchi context coalgebra Γ and discuss the localization in Gorenstein coalgebras. In particular, we describe its Gabriel quiver and carry out some examples when the Morita-Takeuchi context coalgebra is basic.  相似文献
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In this article, we apply the localization techniques to right (*)-serial coalgebras and obtain some interesting results. In particular, we give a characterization of right (*)-serial coalgebras by means of its ‘local structure’, which is the localized right (*)-serial coalgebras, and we get a main result—the periodicity theorem.  相似文献
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