Results 261 to 270 of about 3,105,218 (296)
Some of the next articles are maybe not open access.
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.
openaire +2 more sources
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.
openaire +2 more sources
Centralizer Near-rings, Matrix Near-rings and Cyclic p-Groups
Algebra Colloquium, 2005If G is a finite group and [Formula: see text] is a group of automorphisms of G, then it is known that the matrix near-ring [Formula: see text] is a subnear-ring of the centralizer near-ring [Formula: see text] for every m ≥ 2. Conditions are known under which [Formula: see text] is a proper subnear-ring of [Formula: see text], and if [Formula: see ...
Smith, Kirby C., van Wyk, Leon
openaire +2 more sources
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 ...
openaire +2 more sources
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].
openaire +1 more source
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,
openaire +3 more sources
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,
openaire +3 more sources
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 ...
openaire +2 more sources
On derivations in near-rings and rings
Mathematical Journal of Okayama University, 1992In a near-ring \(R\) a derivation \(D\) is called an scp-derivation if \([x,y] = [D(x), D(y)]\), a Daif 1(2)-derivation if \(D(xy) - D(yx) = [x, y] (=[-x, y])\) (\(\forall x, y \in R\)). Various commutativity (and distributivity) results linked to such derivations are given: e.g.
Bell, Howard E., Mason, Gordon
openaire +3 more sources
Near Majority of Adults Favor R Ratings for Films With Smoking
Ca-A Cancer Journal for Clinicians, 2023Mike Fillon
exaly