• 대한수학회논문집
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• 제34권3호
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• pp.897-910
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• 2019

In this paper we introduce the notion of "robust special Anosov endomorphisms", and show that Anosov endomorphisms of tori which are not neither an Anosov diffeomorphism nor an expanding map, are not robust special.

• East Asian mathematical journal
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• 제32권1호
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• pp.61-75
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• 2016

If ${\phi}$ is a polarizable endomorphism on a projective variety, then the Weil height machine guarantees that ${\phi}$ satisfies Northcott's theorem. In this paper, we show that Northcott's theorem only holds for polarizable endomorphisms and generalize this result to arbitrary dominant endomorphisms: we introduce the height expansion and contraction coefficients which provide weak Northcott's theorem for dominant endomorphisms. We also give some applications of the height expansion and contraction coefficients.

• East Asian mathematical journal
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• 제18권2호
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• pp.245-259
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• 2002

In this paper, all rings or (left)near-rings R are associative, and for near-ring R, all R-groups are right R action and all modules are right R-modules. First, we begin with the study of rings in which all the additive endomorphisms or only the left multiplication endomorphisms are generated by ring endomorphisms and their properties. This study was motivated by the work on the Sullivan's Problem [14]. Next, for any right R-module M, we will introduce AM modules and investigate their basic properties. Finally, for any nearring R, we will also introduce MR-groups and study some of their properties.

• 대한수학회보
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• 제38권1호
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• pp.149-156
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• 2001

In this paper, we initiate the investigation of ring in which all the additive endomorphisms are generated by ring endomorphisms (AGE-rings). This study was motivated by the work on the Sullivan’s Research Problem [11]: Characterize those rings in which every additive endomorphism is a ring endomorphism (AE-rings). The purpose of this paper is to obtain a certain characterization of AGE-rings, and investigate some relations between AGE and LSD-generated rings.

• 대한수학회논문집
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• 제37권3호
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• pp.659-667
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• 2022

This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.

• ETRI Journal
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• 제27권5호
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• pp.617-627
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• 2005

This paper proposes an efficient scalar multiplication algorithm for hyperelliptic curves, which is based on the idea that efficient endomorphisms can be used to speed up scalar multiplication. We first present a new Frobenius expansion method for special hyperelliptic curves that have Gallant-Lambert-Vanstone (GLV) endomorphisms. To compute kD for an integer k and a divisor D, we expand the integer k by the Frobenius endomorphism and the GLV endomorphism. We also present improved scalar multiplication algorithms that use the new expansion method. By our new expansion method, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6 to 28.3 % over the previous algorithms when the algorithms are implemented over finite fields of odd characteristics.

• Korean Journal of Mathematics
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• 제22권2호
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• pp.217-234
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• 2014

Mason extended the reflexive property for subgroups to right ideals, and examined various connections between these and related concepts. A ring was usually called reflexive if the zero ideal satisfies the reflexive property. We here study this property skewed by ring endomorphisms, introducing the concept of an ${\alpha}$-skew reflexive ring, where is an endomorphism of a given ring.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.199-206
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• 2024

The goal of this study is to bring out the following conclusion: Let 𝓡 be a non-commutative prime ring of characteristic not two and 𝓓 be a bi-semiderivation on 𝓡 with a function 𝖋 (surjective). If 𝓓 acts as an endomorphism or as an anti-endomorphism, then 𝓓 = 0 on 𝓡.

• East Asian mathematical journal
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• 제9권2호
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• pp.241-249
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• 1993

• 대한수학회논문집
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• 제9권1호
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• pp.143-146
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• 1994