SOME ASPECTS OF G(H)-RINGS

作者：Sen M K^*; Dasgupta Utpal

来源：Analele Stiintifice ale Universitatii Al I Cuza Din Iasi-Serie Noua-Matematica, 2010, 56(2): 253-272.

• G(H)-ring
• division G(H)-ring
• G(H)-field
• G(H)-ring over rings

In this paper we introduce and study a class of hyperstructure called G(H)-ring. We show that every commutative group admits a G(H)-ring structure. Here we obtain necessary and sufficient conditions for a G(H)-ring to be a division G(H)-ring (and a strong division G(H)-ring). The notion of ideals in a G(H)-ring is also introduced and studied here. We show that every G(H)-ring with an identity set (i.e., an i-set, in short) always contains a maximal ideal. This is obtained that the maximality of an ideal I of a G(H)-ring R with condition (R) (i.e., a multiplicative hyperring with absorbing zero) having an i-set, is a necessary and sufficient condition for the quotient G(H)-ring R/I of R to be a G(H)-field. We establish an isomorphism theorem on G(H)-rings in analogy to the first isomorphism theorem on rings. We construct, over any ring R, a G(H)-ring structure R-A, induced by each A is an element of P* (R) with vertical bar A vertical bar >= 2. We study such G(H)-ring R-A over a ring R, in accordance with the nature of the set A chosen.

• 出版日期2010