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On ternary semifields

Tapan K. Dutta, Sukhendu Kar (2004)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z¯₀.

On the binary system of factors of formal matrix rings

Weining Chen, Guixin Deng, Huadong Su (2020)

Czechoslovak Mathematical Journal

We investigate the formal matrix ring over R defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.

On the category of modules of second kind for Galois coverings

Piotr Dowbor (1996)

Fundamenta Mathematicae

Let F: R → R/G be a Galois covering and m o d 1 ( R / G ) (resp. m o d 2 ( R / G ) ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories ( m o d ( R / G ) ) / [ m o d 1 ( R / G ) ] and m o d 2 ( R / G ) is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.

On the characterization of certain additive maps in prime * -rings

Mohammad Ashraf, Mohammad Aslam Siddeeque, Abbas Hussain Shikeh (2024)

Czechoslovak Mathematical Journal

Let 𝒜 be a noncommutative prime ring equipped with an involution ‘ * ’, and let 𝒬 m s ( 𝒜 ) be the maximal symmetric ring of quotients of 𝒜 . Consider the additive maps and 𝒯 : 𝒜 𝒬 m s ( 𝒜 ) . We prove the following under some inevitable torsion restrictions. (a) If m and n are fixed positive integers such that ( m + n ) 𝒯 ( a 2 ) = m 𝒯 ( a ) a * + n a 𝒯 ( a ) for all a 𝒜 and ( m + n ) ( a 2 ) = m ( a ) a * + n a 𝒯 ( a ) for all a 𝒜 , then = 0 . (b) If 𝒯 ( a b a ) = a 𝒯 ( b ) a * for all a , b 𝒜 , then 𝒯 = 0 . Furthermore, we characterize Jordan left τ -centralizers in semiprime rings admitting an anti-automorphism τ . As applications, we find the structure of...

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