The Coset Group and Com ove Group

§１．　ＢａｓｉｃＤｅｆｉｎｉｔｉｏｎｓＬｅｔＸａｎｄＹｂｅｓｅｔｓ，ｆｏｒａｇｉｖｉｎｇｍａｐｐｉｎｇｆ：Ｘ→Ｙ，ｘ｜→ｙ＝ｆ（ｘ），ａｍａｐｐｉｎｇｆｏｎｐｏｗｅｒｓｅｔｃａｎｂｅｃｏｎｄｕｃｔｅｄｂｙｆ：ｆ：Ｐ（Ｘ）→Ｐ（Ｙ），Ａ｜→Ｂ＝ｆ（Ａ）＝｛ｙ｜ｘ∈Ａ，ｙ＝ｆ（ｘ）｝．　　Ｎｏｔｅｔｈａｔａｂｉｎａｒｙｏｐｅｒａｔｉｏｎｉｓａｓｐｅｃｉａｌｍａｐｐｉｎｇｏｎｓｅｔｓ．ＧｉｖｅｎａｂｉｎａｒｙｏｐｅｒａｔｉｏｎｏｎｓｅｔＸｓｕｃｈｔｈａｔ：：Ｘ×Ｘ→Ｘ，　（ｘ，ｙ）｜→ｘ…     

Group Boolean algebras

ＧｒｏｕｐＢｏｏｌｅａｎＡｌｇｅｂｒａｓＷ．Ｂ．ＶａｅａｎｔｈａＫａｎｄａｓａｍｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＩｎｄｉａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｉｎｄｉａ）ＧｒｏｕｐＢｏｏｌｅａｎＡｌｇｅｂｒａｓ／Ｗ．Ｂ．ＶａｅａｎｔｈａＫａｎ...     

Group Graded Gamma Rings

ＧｒｏｕｐＧｒａｄｅｄＧａｍｍａＲｉｎｇｓＦａｎＦｕｓｈｅｎｇ（樊复生）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｅａｓｔｅｒｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈｅｎｙａｎｇ，１１０００６）ＧｕｏＬｉｎｇｚｈｏｎｇ（郭令忠）（Ｄｅｐａｒｔｍ...     

∗-Prime Group Algebras

An associative algebra R over a field K is said to be right ?-prime if for every nonzero r ? R, there exists a finitely generated subalgebra S of R such that rSt = 0 implies t = 0. Clearly, strongly prime implies ?-prime and ?-prime implies prime. A large number of examples of group algebras are given which show that the concept of ?-prime lies strictly between prime and strongly prime. A complete characterization of ?-prime group algebras is given. It is proved that a group algebra KG of the group G over the field K is ?-prime if and only if Λ⁺(G) = (1). Intersection theorems play an important role in the study. In the process, a new intersection theorem for ?-prime group algebras is obtained. Elementwise characterization of the ?-prime radical is given and its relation with some well-known radicals is discussed.     

Ricci Curvature and Fundamental Group

By refined volume estimates in terms of Ricci curvature, the two results due to J. Milnor (1968) are generalized.     

L-fuzzy Group (Ⅱ)

Ｌ－ｆｕｚｚｙＧｒｏｕｐ（Ⅱ）￥ＪｉａｎｇＢａｏｑｉｎｇ；ＳｕｎＲｏｎｇｇｕａｎｇ（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，４７５００１）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，４７５００１）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｉｓ...     

The Riordan–Dirichlet Group

Mathematical Notes - Riordan matrices are infinite lower triangular matrices corresponing to certain operators in the space of formal power series. In the paper, we introduce analogous matrices for...     

Multiplicative Jordan Decomposition in Integral Group Ring of Group K_8×C_5

In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II.     

Thompson＇s Group F and the Linear Group GL∞（Z）

The authors study the finite decomposition complexity of metric spaces of H, equipped with different metrics, where H is a subgroup of the linear group GL_∞(ℤ). It is proved that there is an injective Lipschitz map φ: (F, d _S ) → (H, d), where F is the Thompson’s group, dS the word-metric of F with respect to the finite generating set S and d a metric of H. But it is not a proper map. Meanwhile, it is proved that φ: (F, d _S ) → (H, d ₁) is not a Lipschitz map, where d ₁ is another metric of H.     

Sem ilinear Equationswith CriticalExponentsonthe Heisenberg Group

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｂｏｕｎｄｅｄｓｍｏｏｔｈｄｏｍａｉｎｉｎｔｈｅＨｅｉｓｅｎｂｅｒｇｇｒｏｕｐＨｎ，ｗｅａｒｅｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｐｒｏｂｌｅｍｏｆｓｅｍｉｌｉｎｅａｒｓｕｂｅｌｌｉｐｔｉｃＬａｐｌａｃｅｅｑｕａｔｉｏｎ－ΔＨｎｕ＝ｕｐ＋ｆ（ｘ，ｕ），ｉｎΩ，ｕ＞０，　　　　ｉｎΩ，（１．１）ｕ＝０，　　　　ｏｎΩ，ｗｈｅｒｅｐｉｓａｒｅａｌｎｕｍｂｅｒ，ｆ（ｘ，ｙ）ｓａｔｉｓｆｉｅｓｓｕｉｔａｂｌｅａｓｓｕｍｐｔｉｏｎｓ（ｓｅｅｂｅｌｏｗｓｅｃｔｉｏ…     

On Strongly π-Regular Group Rings

Let R be an associative ring with unit. An element x R is said to be left (right) -regular if there exist y R and a positive integer n such that . If x is both left and right -regular, then it is said to be strongly -regular. R is said to be a strongly -regular ring if all its elements are strongly -regular. In this paper we determine some conditions which are necessary or sufficient for a group ring to be strongly -regular.AMS Subject Classification (1991): 16E50, 16U99     

The Meta-Grothendieck Group of a Ring

ＴｈｅＭｅｔａ┐ＧｒｏｔｈｅｎｄｉｅｃｋＧｒｏｕｐｏｆａＲｉｎｇ＊）ＦｅｎｇＬｉａｎｇｇｕｉ（冯良贵）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｔｈｅｍａｔｉｃｓ，ＮＵＤＴ，Ｃｈａｎｇｓｈａ，４１００７３）ＡｂｓｔｒａｃｔＷｅｉｎｔｒｏｄｕｃｅｔｈｅｍｅｔａ－Ｇ...     

Group Actions on Hyperbolic 3-manifolds

Suppose M is a nonorientable closed hyperbolic 3-manifold or an orientable closed hyperbolic 3-manifold with odd first Betti number. Then any smooth action of finite cyclic group can be conjugated to preserve the hyperbolic structure. This result supports a main conjecture in 3-manifold theory.     

An Invariant Group of CDF Equation

CDF equation.甲。=甲二二二+2尹呈+6刀2甲:sin22切(1)15 related to the MkdV equationq。=q二二二+6口Zq二(2)(口==一(梦二+叮sinZ尹)or口二切二一刀sinZ甲)[”2],In this PaPer,grouP of CDF equation(1)。we Present an invariant,·t”·‘。,,。W‘·g,尹‘·(。rjf“)二···S·…”‘tr一yP·‘m“‘二‘一“。一“二‘it 15 taken definitely.Lemma If卯15 a solution of(1),then__l/「___。_J、___:_八_._,___八_.。_,___。_c-一叹tl‘U毖乙留“人刀一甲二之匕1“乙甲十甲云GU。乙甲十石,I一co吕乙钾一了I一cUS一乙…     

Strongly Modular Subgroup in Finite Group

Ｓｔｒｏｎｇｌｙ　Ｍｏｄｕｌａｒ　Ｓｕｂｇｒｏｕｐ　ｉｎ　Ｆｉｎｉｔｅ　ＧｒｏｕｐＳｔｒｏｎｇｌｙＭｏｄｕｌａｒＳｕｂｇｒｏｕｐｉｎＦｉｎｉｔｅＧｒｏｕｐ￥ＹｕＪｉａｎｌｉ；ＪｉａｏＤｏｎｇｗｕ（ＬｕｏｙａｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇ...     

The Weil–Petersson Isometry Group

We prove that, for 3g–3+n>1 and (g,n)(1,2), the group of Weil–Petersson isometries of the Teichmüller space T _g,n coincides with the extended mapping class group.     

Group of Self-Equivalences of Sum Object

In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category.     

The Automorphism Group of the Lie Group T（D（V_N,F））

In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.     

Group Codes Defined on Totally Ordered Sets

ＧｒｏｕｐＣｏｄｅｓＤｅｆｉｎｅｄｏｎＴｏｔａｌｌｙＯｒｄｅｒｅｄＳｅｔｓＷａｎＺｈｅｘｉａｎ（万哲先）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ，１０００８０ａｎｄＤｅｐａｒｔｍｅｎｔｏｆＩｎ...     

Semi Group Rings Which are Chinese Ring

In this paper we obtain conditions under which a semigroup ring is a Chinese ring.Further we define what are called weakly Chinese rings and study them.The authors in[1]called a commutative ring R to be a Chinese ring if,given elements a,b∈R and idealI,J(?)R such that a≡b(I J)there exists an element c∈R such that c≡a(I)andc≡b(J).For more properties about Chinese rings please refer[1].