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Lifting of isomorphisms Between Elementary Linear Groups

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Chinese Science Bulletin 1993年第14期38卷 1158-1162页

作者：李福安 Institute of Mathematics Academia Sinica Beijing 100080 PRC

Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved that, if E_m(R) is isomorphic to E_n(A) then m=n (cf. Ref. [1]). When n≥4, every isomorphism E_n(R)E_n(A) is of the standard type, and it can be naturally and uniquely lifted to an isomorphism from St_n(R) to St_n(A) (cf. Refs. [1] and [2]). However, the case n=3 is different from that n≥4,

关键词： linear groups Steinberg groups isomorphisms Dennis-Stein symbols.

Additive Maps Between Standard Operator Algebras Compressing Certain Spectral Functions

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2041-2048页

作者： Jin Chuan HOU Department of Mathematics Shanxi University Taiyuan 030000 P R. China Department of Mathematics Taiyuan University of Technology Taiyuan 030024 P. R. China Department of Mathematics Shanxi University Taiyuan 030000 P. R. China Department of Mathematics Shanxi Normal University Linfen 041004 P. R. China

We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.

关键词： additive maps standard operator algebras spectral functions isomorphisms

On Separable Schur Rings over Abelian Groups

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Algebra Colloquium 2021年第3期28卷 431-440页

作者： Grigory Ryabov Sobolev Institute of Mathematics NovosibirskRussia Novosibirsk State UniversityNovosibirskRussia

A finite group is said to be weakly separable if every algebraic isomorphism between two 5-rings over this group is induced by a combinatorial *** prove that every abelian weakly separable group only belongs to one of... 详细信息

关键词： isomorphisms Schur rings abelian groups

Skew Incidence Rings and the Isomorphism Problem

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Algebra Colloquium 2022年第3期29卷 419-426页

作者： Érica Z.Fornaroli Departamento de Matemática Universidade Estadual de Maringá Maringá-PRCEP:87020-900Brazil

Let X be a finite partially ordered set,R an associative unital ring andσan endomorphism of *** describe some properties of the skew incidence ring I(X,R,σ)such as invertible elements,idempotents,the Jacobson radical and the ***,if two skew incidence rings I(X,R,σ)and I(Y,S,τ)are isomorphic and the only idempotents of R and S are the trivial ones,we show that the partially ordered sets X and Y are isomorphic.

关键词： units idempotents Jacobson radical center isomorphisms

Isomorphic Commutative Group Algebras of p-Mixed Warfield Groups

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Acta Mathematica Sinica,English Series 2005年第4期21卷 913-916页

作者： PeterV.DANCHEV 13 General Kutuzov StreetBlock 7Floor 2Apartment 44003 PlovdivBulgaria

Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a r... 详细信息

关键词： p-mixed Warfield groups Isotype subgroups Heights Bases isomorphisms