# Deductive systems of a cone algebra (Part 1): Semi-$\ell g$-cones

In: Mathematica Slovaca, vol. 58, no. 6
N. V. Subrahmanyam

## Details:

Year, pages: 2008, 653 - 670
Keywords:
cone algebra, semi-$\ell$g-cone, pseudo MV-algebra, deductive system, $\ell$-group, ideal
A semi-$\ell$g-cone is an algebra $(C; *, : , · )$ of type $(2, 2, 2)$ satisfying the equations $(a * a) * b = b = b : (a : a)$; $a *(b : c) = (a * b) : c$; $a : (b * a) = (b : a) * b$ and $(ab) * c = b * (a * c)$. An $\ell$-group cone is a semi-$\ell$g-cone and a bounded semi-$\ell$g-cone is term equivalent to a pseudo MV-algebra. Also, a subset $A$ of a semi-$\ell$g-cone $C$ is an ideal of $C$ if and only if it is a deductive system of its reduct $(C; *, : )$.
Subrahmanyam, N. 2008. Deductive systems of a cone algebra (Part 1): Semi-$\ell g$-cones. In Mathematica Slovaca, vol. 58, no.6, pp. 653-670. 0139-9918.
Subrahmanyam, N. (2008). Deductive systems of a cone algebra (Part 1): Semi-$\ell g$-cones. Mathematica Slovaca, 58(6), 653-670. 0139-9918.