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n -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

Let R be a graded ring and n 1 an integer. We introduce and study n -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that n -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be m -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever n > m . Many properties of the n -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate...

Natural endomorphisms of quasi-shuffle Hopf algebras

Jean-Christophe Novelli, Frédéric Patras, Jean-Yves Thibon (2013)

Bulletin de la Société Mathématique de France

The Hopf algebra of word-quasi-symmetric functions ( 𝐖𝐐𝐒𝐲𝐦 ), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the other operations on 𝐖𝐐𝐒𝐲𝐦 . This extends constructions familiar and central in the theory of free Lie algebras, noncommutative symmetric functions and their various applications fields, and allows to interpret 𝐖𝐐𝐒𝐲𝐦 as a convolution algebra of linear endomorphisms of quasi-shuffle...

Non-commutative separability and group actions.

Ricardo Alfaro (1992)

Publicacions Matemàtiques

We give conditions for the skew group ring S * G to be strongly separable and H-separable over the ring S. In particular we show that the H-separability is equivalent to S being central Galois extension. We also look into the H-separability of the ring S over the fixed subring R under a faithful action of a group G. We show that such a chain: S * G H-separable over S and S H-separable over R cannot occur, and that the centralizer of R in S is an Azumaya algebra in the presence of a central element...

Nonlinear * -Lie higher derivations of standard operator algebras

Mohammad Ashraf, Shakir Ali, Bilal Ahmad Wani (2018)

Communications in Mathematics

Let be an infinite-dimensional complex Hilbert space and 𝔄  be a standard operator algebra on which is closed under the adjoint operation. It is shown that every nonlinear * -Lie higher derivation 𝒟 = { δ n } n of 𝔄 is automatically an additive higher derivation on 𝔄 . Moreover, 𝒟 = { δ n } n is an inner * -higher derivation.

Non-transitive generalizations of subdirect products of linearly ordered rings

Jiří Rachůnek, Dana Šalounová (2003)

Czechoslovak Mathematical Journal

Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-rings having...

Normability of an S-ring.

El-Miloudi Marhrani, Mohamed Aamri (1998)

Collectanea Mathematica

We give some criteria of normability of an S-ring, and we study the properties of its norms.

Notes on slender prime rings

Robert El Bashir, Tomáš Kepka (1996)

Commentationes Mathematicae Universitatis Carolinae

If R is a prime ring such that R is not completely reducible and the additive group R ( + ) is not complete, then R is slender.

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