On the Structure of Quaternion Rings Over $${\mathbb{Z}/n\mathbb{Z}}$$ Z / n Z

2015 ◽  
Vol 25 (4) ◽  
pp. 875-887 ◽  
Author(s):  
José María Grau ◽  
Celino Miguel ◽  
Antonio M. Oller-Marcén
Keyword(s):  
Quaternion Rings

scholarly journals Cayley–Dickson process and centrally essential rings

2019 ◽  
Vol 18 (12) ◽  
pp. 1950229 ◽  
Author(s):  
V. T. Markov ◽  
A. A. Tuganbaev
Keyword(s):  
Quaternion Rings ◽  
Generalized Quaternion

We describe associative center [Formula: see text] and the center [Formula: see text] of the ring [Formula: see text] obtained by applying the generalized Cayley–Dickson construction and we find conditions under which the ring [Formula: see text] is [Formula: see text]-essential or centrally essential. The obtained results are applied to generalized quaternion rings and octonion rings; we use them to construct an example of a nonassociative centrally essential ring.

scholarly journals Cayley–Dickson process and centrally essential rings

2019 ◽  
Vol 19 (05) ◽  
pp. 2050096
Author(s):  
V. T. Markov ◽  
A. A. Tuganbaev
Keyword(s):  
Quaternion Rings ◽  
Generalized Quaternion

We describe associative center [Formula: see text] and the center [Formula: see text] of the ring [Formula: see text] obtained by applying the generalized Cayley–Dickson construction and we find conditions under which the ring [Formula: see text] is [Formula: see text]-essential or centrally essential. The obtained results are applied to generalized quaternion rings and octonion rings; we use them to construct an example of a nonassociative centrally essential ring.

scholarly journals Tripotent elements in quaternion rings over ℤp

2021 ◽  
Vol 13 (1) ◽  
pp. 78-87
Author(s):  
Michael Aristidou ◽  
Kidus Hailemariam
Keyword(s):  
Finite Ring ◽  
Quaternion Rings

Abstract In this paper, we discuss tripotent1 elements in the finite ring ℍ/ℤp. We provide examples and establish conditions for tripotency. We follow similar methods used in [3] for idempotent elements in ℍ/ℤp.

Convolution Rings

2006 ◽  
Vol 13 (02) ◽  
pp. 211-238 ◽  
Author(s):  
Stefan Veldsman
Keyword(s):  
Convolution Type ◽  
Group Rings ◽  
Incidence Algebras ◽  
Quaternion Rings

The notion of a convolution type is introduced. Imposing such a type on a ring gives the corresponding convolution ring. Under this umbrella, a wide variety of ring constructions can be covered, including polynomials, matrices, incidence algebras, necklace rings, group rings and quaternion rings. Here the influence of the convolution type on the corresponding convolution ring is investigated, in particular on the existence of homomorphisms and ideals.

Quaternion rings and octonion rings

2016 ◽  
Vol 12 (1) ◽  
pp. 143-155
Author(s):  
Gangyong Lee ◽  
Kiyoichi Oshiro
Keyword(s):  
Quaternion Rings
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