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Certain partitions on a set and their applications to different classes of graded algebras

Antonio J. Calderón Martín, Boubacar Dieme (2021)

Communications in Mathematics

Let ( 𝔄 , ϵ u ) and ( 𝔅 , ϵ b ) be two pointed sets. Given a family of three maps = { f 1 : 𝔄 𝔄 ; f 2 : 𝔄 × 𝔄 𝔄 ; f 3 : 𝔄 × 𝔄 𝔅 } , this family provides an adequate decomposition of 𝔄 { ϵ u } as the orthogonal disjoint union of well-described -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak H * -algebras.

Certain simple maximal subfields in division rings

Mehdi Aaghabali, Mai Hoang Bien (2019)

Czechoslovak Mathematical Journal

Let D be a division ring finite dimensional over its center F . The goal of this paper is to prove that for any positive integer n there exists a D ( n ) , the n th multiplicative derived subgroup such that F ( a ) is a maximal subfield of D . We also show that a single depth- n iterated additive commutator would generate a maximal subfield of D .

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