Results 261 to 270 of about 3,104,614 (297)
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Canadian Journal of Mathematics, 1969
The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
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The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
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Embedding of a Near-Ring into a Near-Ring with Identity
1987It is well known, that an arbitrary near-ring N may be embedded into a near-ring N with identity. Details and references are to be found, e.g., in [3; § 1, section c]. Also, it is very well known, that any ring A is an ideal of a ring A* with identity [2; p. 11].
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NEW KINDS OF NEAR-RINGS FROM OLD NEAR RINGS
JP Journal of Algebra, Number Theory and Applications, 2018Summary: In this paper, we construct that a new kind of near-ring, that is, \((e, t)\)-near-ring \((R, +,\ast)\) with given addition in \(R\) and new multiplication \(\ast\) which is expressed in terms of the original multiplication and addition by defining \(a\ast b\) to be a polynomial in \(a\) and \(b\), from a given near-ring \((R, +, \cdot ...
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Mathematical Journal of Okayama University, 1990
Let \(N\) denote a zero-symmetric left near-ring, \(A\) a nonzero ideal of \(N\), and \(d\) a derivation on \(N\). The author proves several theorems on additive or multiplicative commutativity of \(N\), extending results of the reviewer and \textit{G. Mason} [Near-rings and near-fields, Proc. Conf., Tübingen, F.R.G. 1985, North-Holland Math. Stud. 137,
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Let \(N\) denote a zero-symmetric left near-ring, \(A\) a nonzero ideal of \(N\), and \(d\) a derivation on \(N\). The author proves several theorems on additive or multiplicative commutativity of \(N\), extending results of the reviewer and \textit{G. Mason} [Near-rings and near-fields, Proc. Conf., Tübingen, F.R.G. 1985, North-Holland Math. Stud. 137,
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Near-rings whose laminated near-rings are Boolean
九州大学教養部数学雑誌, 1987In [Proc. Edinb. Math. Soc., II. Ser. 23, 97-102 (1980; Zbl 0415.16028)] \textit{K. D. Magill, jun.} introduced the concept of a laminated near-ring. Let N be an arbitrary near-ring. Each element a in N yields a new near- ring \(N_ a\) whose additive group coincides with that of N and whose multiplication * is defined by \(x*y=xay\) for any two ...
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2007
This volume consists of seven papers related in various matters to the research work of Kostia Beidar, a distinguished ring theorist and professor of National Ching Kung University (NCKU). Written by leading experts in these areas, the papers also emphasize important applications to other fields of mathematics.
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This volume consists of seven papers related in various matters to the research work of Kostia Beidar, a distinguished ring theorist and professor of National Ching Kung University (NCKU). Written by leading experts in these areas, the papers also emphasize important applications to other fields of mathematics.
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Quantitative Logic and Soft Computing, 2012
Songfa You, Ming Cao, Yijun Feng
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Songfa You, Ming Cao, Yijun Feng
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