Displaying similar documents to “Certain simple maximal subfields in division rings”

Maximal non λ -subrings

Rahul Kumar, Atul Gaur (2020)

Czechoslovak Mathematical Journal

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Let R be a commutative ring with unity. The notion of maximal non λ -subrings is introduced and studied. A ring R is called a maximal non λ -subring of a ring T if R T is not a λ -extension, and for any ring S such that R S T , S T is a λ -extension. We show that a maximal non λ -subring R of a field has at most two maximal ideals, and exactly two if R is integrally closed in the given field. A determination of when the classical D + M construction is a maximal non λ -domain is given. A necessary condition...

Maximal non-pseudovaluation subrings of an integral domain

Rahul Kumar (2024)

Czechoslovak Mathematical Journal

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The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let R S be an extension of domains. Then R is called a maximal non-pseudovaluation subring of S if R is not a pseudovaluation subring of S , and for any ring T such that R T S , T is a pseudovaluation subring of S . We show that if S is not local, then there no such T exists between R and S . We also characterize maximal non-pseudovaluation subrings of a local integral domain.

Semicommutativity of the rings relative to prime radical

Handan Kose, Burcu Ungor (2015)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we introduce a new kind of rings that behave like semicommutative rings, but satisfy yet more known results. This kind of rings is called P -semicommutative. We prove that a ring R is P -semicommutative if and only if R [ x ] is P -semicommutative if and only if R [ x , x - 1 ] is P -semicommutative. Also, if R [ [ x ] ] is P -semicommutative, then R is P -semicommutative. The converse holds provided that P ( R ) is nilpotent and R is power serieswise Armendariz. For each positive integer n , R is P -semicommutative...

Remarks on L B I -subalgebras of C ( X )

Mehdi Parsinia (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let A ( X ) denote a subalgebra of C ( X ) which is closed under local bounded inversion, briefly, an L B I -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of A ( X ) , we generalize the notion of z A β -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of C ( X ) ...

Augmentation quotients for Burnside rings of generalized dihedral groups

Shan Chang (2016)

Czechoslovak Mathematical Journal

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Let H be a finite abelian group of odd order, 𝒟 be its generalized dihedral group, i.e., the semidirect product of C 2 acting on H by inverting elements, where C 2 is the cyclic group of order two. Let Ω ( 𝒟 ) be the Burnside ring of 𝒟 , Δ ( 𝒟 ) be the augmentation ideal of Ω ( 𝒟 ) . Denote by Δ n ( 𝒟 ) and Q n ( 𝒟 ) the n th power of Δ ( 𝒟 ) and the n th consecutive quotient group Δ n ( 𝒟 ) / Δ n + 1 ( 𝒟 ) , respectively. This paper provides an explicit -basis for Δ n ( 𝒟 ) and determines the isomorphism class of Q n ( 𝒟 ) for each positive integer n .

Strongly 2-nil-clean rings with involutions

Huanyin Chen, Marjan Sheibani Abdolyousefi (2019)

Czechoslovak Mathematical Journal

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A * -ring R is strongly 2-nil- * -clean if every element in R is the sum of two projections and a nilpotent that commute. Fundamental properties of such * -rings are obtained. We prove that a * -ring R is strongly 2-nil- * -clean if and only if for all a R , a 2 R is strongly nil- * -clean, if and only if for any a R there exists a * -tripotent e R such that a - e R is nilpotent and e a = a e , if and only if R is a strongly * -clean SN ring, if and only if R is abelian, J ( R ) is nil and R / J ( R ) is * -tripotent. Furthermore, we explore...

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

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Let R and S be commutative rings with unity, f : R S a ring homomorphism and J an ideal of S . Then the subring R f J : = { ( a , f ( a ) + j ) a R and j J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R f J is a (generalized) filter ring.

Annihilating and power-commuting generalized skew derivations on Lie ideals in prime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

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Let R be a prime ring of characteristic different from 2 and 3, Q r its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n 1 a fixed positive integer. Let α be an automorphism of the ring R . An additive map D : R R is called an α -derivation (or a skew derivation) on R if D ( x y ) = D ( x ) y + α ( x ) D ( y ) for all x , y R . An additive mapping F : R R is called a generalized α -derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F ( x y ) = F ( x ) y + α ( x ) D ( y ) for all x , y R . We prove...

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Moshe Marcus, Laurent Véron (2004)

Journal of the European Mathematical Society

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Let Ω be a bounded domain of class C 2 in N and let K be a compact subset of Ω . Assume that q ( N + 1 ) / ( N 1 ) and denote by U K the maximal solution of Δ u + u q = 0 in Ω which vanishes on Ω K . We obtain sharp upper and lower estimates for U K in terms of the Bessel capacity C 2 / q , q ' and prove that U K is σ -moderate. In addition we describe the precise asymptotic behavior of U K at points σ K , which depends on the “density” of K at σ , measured in terms of the capacity C 2 / q , q ' .

C * -points vs P -points and P -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

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In a Tychonoff space X , the point p X is called a C * -point if every real-valued continuous function on C { p } can be extended continuously to p . Every point in an extremally disconnected space is a C * -point. A classic example is the space 𝐖 * = ω 1 + 1 consisting of the countable ordinals together with ω 1 . The point ω 1 is known to be a C * -point as well as a P -point. We supply a characterization of C * -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

On extending C k functions from an open set to with applications

Walter D. Burgess, Robert M. Raphael (2023)

Czechoslovak Mathematical Journal

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For k { } and U open in , let C k ( U ) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f C k ( U ) there is g C ( ) with U coz g and h C k ( ) with f g | U = h | U . The function f and its k derivatives are not assumed to be bounded on U . The function g is constructed using splines based on the Mollifier function. Some consequences about the ring C k ( ) are deduced from this, in particular that Q cl ( C k ( ) ) = Q ( C k ( ) ) .

On the conjugate type vector and the structure of a normal subgroup

Ruifang Chen, Lujun Guo (2022)

Czechoslovak Mathematical Journal

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Let N be a normal subgroup of a group G . The structure of N is given when the G -conjugacy class sizes of N is a set of a special kind. In fact, we give the structure of a normal subgroup N under the assumption that the set of G -conjugacy class sizes of N is ( p 1 n 1 a 1 n 1 , , p 1 1 a 11 , 1 ) × × ( p r n r a r n r , , p r 1 a r 1 , 1 ) , where r > 1 , n i > 1 and p i j are distinct primes for i { 1 , 2 , , r } , j { 1 , 2 , , n i } .