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2. Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra
- Creator:
- Ammar, Faouzi, Makhlouf, Abdenacer, and Saadaoul, Nejib
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Hom-Lie superalgebra, derivation, cohomology, and $q$-deformed superalgebra
- Language:
- English
- Description:
- Hom-Lie algebra (superalgebra) structure appeared naturally in $q$-deformations, based on $\sigma $-derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of $\alpha ^k$-derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted ${\rm osp}(1,2)$ superalgebra and $q$-deformed Witt superalgebra.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. Constructions preserving n-weak amenability of Banach algebras
- Creator:
- Jabbari, A., Moslehian, Sal Mohammad, and Vishki, H. R. E.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- weak amenability, n-weak amenability, derivation, second dual, direct sum, Banach algebra, and Arens product
- Language:
- English
- Description:
- A surjective bounded homomorphism fails to preserve n-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. Derivations with Engel conditions in prime and semiprime rings
- Creator:
- Huang, Shuliang
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- prime and semiprime rings, ideal, derivation, and GPIs
- Language:
- English
- Description:
- Let $R$ be a prime ring, $I$ a nonzero ideal of $R$, $d$ a derivation of $R$ and $m, n$ fixed positive integers. (i) If $(d[x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. (ii) If $\mathop {\rm Char}R\neq 2$ and $[d(x),d(y)]_{m}=[x,y]^{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover, we also examine the case when $R$ is a semiprime ring.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. Derivations with power central values on Lie ideals in prime rings
- Creator:
- Dhara, Basudeb and Sharma, Rajendra K.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- prime ring, derivation, extended centroid, and martindale quotient ring
- Language:
- English
- Description:
- Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. Free actions on semiprime rings
- Creator:
- Chaudhry, Muhammad Anwar and Samman, Mohammad S.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- prime ring, semiprime ring, dependent element, free action, centralizer, and derivation
- Language:
- English
- Description:
- We identify some situations where mappings related to left centralizers, derivations and generalized (α, β)-derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation T, of a semiprime ring R the mapping ψ: R → R defined by ψ(x) = T(x)x − xT(x) for all x ∈ R is a free action. We also show that for a generalized (α, β)-derivation F of a semiprime ring R, with associated (α, β)-derivation d, a dependent element a of F is also a dependent element of α + d. Furthermore, we prove that for a centralizer f and a derivation d of a semiprime ring R, ψ = d ◦ f is a free action.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
7. Generalized derivations on Lie ideals in prime rings
- Creator:
- Dhara, Basudeb, Kar, Sukhendu, and Mondal, Sachhidananda
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring, Lie ideal, and Banach algebra
- Language:
- English
- Description:
- Let $R$ be a prime ring with its Utumi ring of quotients $U$ and extended centroid $C$. Suppose that $F$ is a generalized derivation of $R$ and $L$ is a noncentral Lie ideal of $R$ such that $F(u)[F(u),u]^n=0$ for all $u \in L$, where $n\geq 1$ is a fixed integer. Then one of the following holds: \begin {itemize} \item [(1)] there exists $\lambda \in C$ such that $F(x)=\lambda x$ for all $x\in R$; \item [(2)] $R$ satisfies $s_4$ and $F(x)=ax+xb$ for all $x\in R$, with $a, b\in U$ and $a-b\in C$; \item [(3)] $\mathop {\rm char}(R)=2$ and $R$ satisfies $s_4$. \end {itemize} As an application we also obtain some range inclusion results of continuous generalized derivations on Banach algebras.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8. Kompozice a její potenciál v současné slovní zásobě češtiny
- Creator:
- Bozděchová, Ivana
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- composition, compound-word, derivation, derived-word, deverbative names of persons, kompozice, kompozitum, derivace, derivát, and deverbativní názvy osob
- Language:
- Czech
- Description:
- Along with derivation, composition represents the second most important word-formative process in Czech, primarily with certain names (such as professional terms). The paper deals with two specific word-formative types of deverbative names of persons, traditionally referred to as nouns of agents (nomina agentis) -compounds with suffixes -tel and -č. These compound names, excerpted from the Czech National Corpus (SYN2010) and confronted with Czech dictionaries (including neologisms), are compared with parallel derived-names, namely in terms of onomasiological and semantic functions of their constituent parts. Their systemic and empirical (textual) productivity (based on corpora) is further considered. Presented analysis is a part of larger research of Czech compounds conducted currently by the author.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
9. Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings
- Creator:
- Bhat, Vijay Kumar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Ore extension, automorphism, derivation, minimal prime, pseudo-valuation ring, and near pseudo-valuation ring
- Language:
- English
- Description:
- Let $R$ be a ring. We recall that $R$ is called a near pseudo-valuation ring if every minimal prime ideal of $R$ is strongly prime. Let now $\sigma $ be an automorphism of $R$ and $\delta $ a $\sigma $-derivation of $R$. Then $R$ is said to be an almost $\delta $-divided ring if every minimal prime ideal of $R$ is $\delta $-divided. Let $R$ be a Noetherian ring which is also an algebra over $\mathbb {Q}$ ($\mathbb {Q}$ is the field of rational numbers). Let $\sigma $ be an automorphism of $R$ such that $R$ is a $\sigma (*)$-ring and $\delta $ a $\sigma $-derivation of $R$ such that $\sigma (\delta (a)) = \delta (\sigma (a))$ for all $a \in R$. Further, if for any strongly prime ideal $U$ of $R$ with $\sigma (U) = U$ and $\delta (U)\subseteq \delta $, $U[x; \sigma , \delta ]$ is a strongly prime ideal of $R[x; \sigma , \delta ]$, then we prove the following: (1) $R$ is a near pseudo valuation ring if and only if the Ore extension $R[x; \sigma ,\delta ]$ is a near pseudo valuation ring. (2) $R$ is an almost $\delta $-divided ring if and only if $R[x;\sigma ,\delta ]$ is an almost $\delta $-divided ring.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
10. Názvy dokumentů - aspekt slovotvorný
- Creator:
- Vondráček, Miloslav
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- derivation, suffix, motivation, founding, derivace, sufix, motivace, and fundace
- Language:
- Czech
- Description:
- The article presents a survey of the word-formation means used for the derivation of titles of documents. The focus is placed on the relationship between the semantic motivation and formal founding. The text tries to capture the extent of analogy of word-formation processes on the background of the relationship of langue and parole.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public