• Honam Mathematical Journal
• /
• v.36 no.4
• /
• pp.863-884
• /
• 2014

In this paper, we introduce a coupled $\mathcal{N}$-structure which is the generalization of $\mathcal{N}$-structure. Using this coupled $\mathcal{N}$-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal. Also the characterization of coupled $\mathcal{N}$-ideal is presented.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.431-439
• /
• 2012

Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.417-437
• /
• 2009

The notions of $\mathcal{N}$-subalgebras, (closed, commutative, retrenched) $\mathcal{N}$-ideals, $\theta$-negative functions, and $\alpha$-translations are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (commutative) $\mathcal{N}$-ideal are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and commutative $\mathcal{N}$-ideal are discussed. We verify that every $\alpha$-translation of an $\mathcal{N}$-subalgebra (resp. $\mathcal{N}$-ideal) is a retrenched $\mathcal{N}$-subalgebra (resp. retrenched $\mathcal{N}$-ideal).