Sultam Thioureas Synthesized via an Alternative Ring-Forming Reaction

2015 ◽  
Vol 45 (9) ◽  
pp. 1055-1067 ◽  
Author(s):  
Victoria Li ◽  
Diane N. Le ◽  
Edward J. Valente ◽  
Warren J. L. Wood
Keyword(s):  
Alternative Ring

Commutative center = center in a prime finitely generated right alternative ring

1997 ◽  
Vol 25 (10) ◽  
pp. 3147-3153 ◽  
Author(s):  
Irvin R. Hentzel ◽  
Erwin Kleinfeld ◽  
Harry F. Smith
Keyword(s):  
Finitely Generated ◽  
Alternative Ring ◽  
Right Alternative Ring

scholarly journals The socle of an alternative ring

1970 ◽  
Vol 14 (4) ◽  
pp. 443-463 ◽  
Author(s):  
M Slater
Keyword(s):  
Alternative Ring

scholarly journals RIGHT NUCLEUS IN GENERALIZED RIGHT ALTERNATIVE RINGS

2015 ◽  
Vol 3 (1) ◽  
pp. 1-12
Author(s):  
Jayalakshmi ◽  
S. Madhavi Latha
Keyword(s):  
Alternative Algebra ◽  
Finitely Generated ◽  
Alternative Ring ◽  
Locally Nilpotent ◽  
The Right ◽  
Right Alternative Ring

Some properties of the right nucleus in generalized right alternative rings have been presented in this paper. In a generalized right alternative ring R which is finitely generated or free of locally nilpotent ideals, the right nucleus Nr equals the center C. Also, if R is prime and Nr ¹ C, then the associator ideal of R is locally nilpotent. Seong Nam [5] studied the properties of the right nucleus in right alternative algebra. He showed that if R is a prime right alternative algebra of char. ≠ 2 and Right nucleus Nr is not equal to the center C, then the associator ideal of R is locally nilpotent. But the problem arises when it come with the study of generalized right alternative ring as the ring dose not absorb the right alternative identity. In this paper we consider our ring to be generalized right alternative ring and try to prove the results of Seong Nam [5]. At the end of this paper we give an example to show that the generalized right alternative ring is not right alternative.

Some Radical Properties of Jordan Matrix Rings

1979 ◽  
Vol 31 (1) ◽  
pp. 189-196
Author(s):  
Michael Rich
Keyword(s):  
Unique Solution ◽  
Identity Element ◽  
Alternative Ring ◽  
Matrix Rings ◽  
Jordan Ring ◽  
Jordan Matrix ◽  
Image Position ◽  
Canonical Involution

Let A be a ring (not necessarily associative) in which 2x = a has a unique solution for each a ∈ A. Then it is known that if A contains an identity element 1 and an involution j : x ↦ x and if Ja is the canonical involution on An determined by where the ai al−l, 1 ≦ i ≦ n are symmetric elements in the nucleus of A then H(An, Ja), the set of symmetric elements of An, for n ≧ 3 is a Jordan ring if and only if either A is associative or n = 3 and A is an alternative ring whose symmetric elements lie in its nucleus [2, p. 127].

scholarly journals Some properties of the Levitzki radical in alternative rings

1982 ◽  
Vol 32 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Michael Rich
Keyword(s):  
Nilpotent Ideal ◽  
Finitely Generated ◽  
Alternative Ring ◽  
Locally Nilpotent ◽  
Torsion Free

AbstractTwo local nilpotent properties of an associative or alternative ringAcontaining an idempotent are shown. First, ifA=A11+A10+A01+A00is the Peirce decomposition ofArelative toethen ifais associative or semiprime alternative and 3-torsion free then any locally nilpotent idealBofAiigenerates a locally nilpotent ideal 〈B〉 ofA. As a consequenceL(Aii) =Aii∩L(A)for the Levitzki radicalL. Also bounds are given for the index of nilpotency of any finitely generated subring of 〈B〉. Second, ifA(x)denotes a homotope ofAthenL(A)⊆L(A(x))and, in particular, ifA(x)is an isotope ofAthenL(A)=L(A(x)).

Neurosteroid Analogues. 11. Alternative Ring System Scaffolds:  γ-Aminobutyric Acid Receptor Modulation and Anesthetic Actions of Benz[f]indenes

2006 ◽  
Vol 49 (15) ◽  
pp. 4595-4605 ◽  
Author(s):  
Jamie B. Scaglione ◽  
Brad D. Manion ◽  
Ann Benz ◽  
Amanda Taylor ◽  
Gregory T. DeKoster ◽  
...  
Keyword(s):  
Ring System ◽  
Aminobutyric Acid ◽  
Alternative Ring ◽  
Acid Receptor ◽  
Receptor Modulation

scholarly journals A Road Network for Freight Transport in Flanders: Multi-Actor Multi-Criteria Assessment of Alternative Ring Ways

2013 ◽  
Vol 5 (10) ◽  
pp. 4222-4246 ◽  
Author(s):  
Levi Vermote ◽  
Cathy Macharis ◽  
Koen Putman
Keyword(s):  
Road Network ◽  
Freight Transport ◽  
Alternative Ring

Nilpotent Ideals in Alternative Rings

1980 ◽  
Vol 23 (3) ◽  
pp. 299-303 ◽  
Author(s):  
Michael Rich
Keyword(s):  
Upper Bound ◽  
Associative Ring ◽  
Analogous Result ◽  
Alternative Ring ◽  
Locally Nilpotent ◽  
Open Question ◽  
The Ideal

It is well known and immediate that in an associative ring a nilpotent one-sided ideal generates a nilpotent two-sided ideal. The corresponding open question for alternative rings was raised by M. Slater [6, p. 476]. Hitherto the question has been answered only in the case of a trivial one-sided ideal J (i.e., in case J2 = 0) [5]. In this note we solve the question in its entirety by showing that a nilpotent one-sided ideal K of an alternative ring generates a nilpotent two-sided ideal. In the process we find an upper bound for the index of nilpotency of the ideal generated. The main theorem provides another proof of the fact that a semiprime alternative ring contains no nilpotent one-sided ideals. Finally we note the analogous result for locally nilpotent one-sided ideals.

On Nilpotent Finite Alternative Rings with Planar Zero-Divisor Graphs

2016 ◽  
Vol 23 (04) ◽  
pp. 657-661
Author(s):  
A. S. Kuzmina
Keyword(s):  
Zero Divisor ◽  
Alternative Ring ◽  
Zero Divisor Graph

In this paper we prove that any finite nilpotent alternative ring with planar zero-divisor graph is associative.

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