ON REGULAR TERNARY SEMIHYPERGROUPS

HILA, KOSTAQ; NAKA, KRISANTHI

AKTET - Journal of Institute Alb-Shkenca
AKTET, Volume 4, Issue 3, Matematike, Statistike, 2011

Title: ON REGULAR TERNARY SEMIHYPERGROUPS

Titulli shqip: MBI GJYSMEHIPERGRUPET E RREGULLT TERNAR

Abstract: This paper deals with a class of algebraic hypersystems which represent a generalization of semigroups and hypersemigroups. This class of of hypersystems is called ternary semihypergroups. The notion of regularity of different type of algebraic systems has been introduced and characterized by different authors such as Neumann, Iseki, Kovacs, Lajos etc. Different authors have studied the notion of regularity in ternary algebraic systems. In this paper we generalize this notion in ternary semihypergroups and we study some interesting properties of regular ternary semihypergroups, completely regular ternary semihypergroups, intra-regular ternary semihypergroups and characterize them by using various hyperideals of ternary semihypergroups.

Abstrakti: Ky artikull merret me nje klase te hipersistemeve algjebrike e cila paraqet nje pergjithesim te gjysmegrupeve dhe gjysmehipergrupeve. Kjo klase e hipersitemeve algjebrike Kjo klase e hipersistemeve quhet gjysmehipergrupet ternare. Koncepti i rregullsise se tipeve te ndryshme te sistemeve algjebrike eshte prezantuar, studiuar dhe karakterizuar nga autore te ndryshem si p.sh. Neumann, Iseki, Kovacs, Lajos etj. Autore te ndryshem kane studiuar konceptin e rregullsise ne sistemet ternare algjebrike. Ne kete artikull ne pergjithesojme kete koncept ne gjysmehipergrupet ternare dhe studiojme disa veti interesante te gjysmehipergrupeve ternare te rregullt, te gjysmehipergrupeve ternare plotesisht te rregullt, te gjysmehipergrupeve ternare intra te rregullt dhe i karakterizojme ata duke perdorur hiperideale te ndryshem te gjysmehipergrupeve ternare.

Key words: ternary semihypergroup, hyperideal, completely-regular, intra-regular, regular, completely-semiprime

Fjalë kyçe: gjysmehipergrup ternar, hiperideal, plotesisht-i-rregullt, intra-i-regullt, rregullt, plotesisht-semiprim

Corresponding author: KOSTAQ HILA (kostaq_hila@yahoo.com)

Authors: KOSTAQ HILA, UNIVERSITY OF GJIROKASTRA, Gjirokastër, Albania
KRISANTHI NAKA, UNIVERSITY OF GJIROKASTRA, Gjirokastër, Albania

Full text: Download Issue 3 [PDF]

	AKTET Journal of Institute Alb-Shkenca Revistë Shkencore e Institutit Alb-Shkenca ( ISSN 2073-2244 )
(english)

Title:	ON REGULAR TERNARY SEMIHYPERGROUPS
Titulli shqip:	MBI GJYSMEHIPERGRUPET E RREGULLT TERNAR
Abstract:	This paper deals with a class of algebraic hypersystems which represent a generalization of semigroups and hypersemigroups. This class of of hypersystems is called ternary semihypergroups. The notion of regularity of different type of algebraic systems has been introduced and characterized by different authors such as Neumann, Iseki, Kovacs, Lajos etc. Different authors have studied the notion of regularity in ternary algebraic systems. In this paper we generalize this notion in ternary semihypergroups and we study some interesting properties of regular ternary semihypergroups, completely regular ternary semihypergroups, intra-regular ternary semihypergroups and characterize them by using various hyperideals of ternary semihypergroups.
Abstrakti:	Ky artikull merret me nje klase te hipersistemeve algjebrike e cila paraqet nje pergjithesim te gjysmegrupeve dhe gjysmehipergrupeve. Kjo klase e hipersitemeve algjebrike Kjo klase e hipersistemeve quhet gjysmehipergrupet ternare. Koncepti i rregullsise se tipeve te ndryshme te sistemeve algjebrike eshte prezantuar, studiuar dhe karakterizuar nga autore te ndryshem si p.sh. Neumann, Iseki, Kovacs, Lajos etj. Autore te ndryshem kane studiuar konceptin e rregullsise ne sistemet ternare algjebrike. Ne kete artikull ne pergjithesojme kete koncept ne gjysmehipergrupet ternare dhe studiojme disa veti interesante te gjysmehipergrupeve ternare te rregullt, te gjysmehipergrupeve ternare plotesisht te rregullt, te gjysmehipergrupeve ternare intra te rregullt dhe i karakterizojme ata duke perdorur hiperideale te ndryshem te gjysmehipergrupeve ternare.
Key words:	ternary semihypergroup, hyperideal, completely-regular, intra-regular, regular, completely-semiprime
Fjalë kyçe:	gjysmehipergrup ternar, hiperideal, plotesisht-i-rregullt, intra-i-regullt, rregullt, plotesisht-semiprim
Corresponding author:	KOSTAQ HILA (kostaq_hila@yahoo.com)
Authors:	KOSTAQ HILA, UNIVERSITY OF GJIROKASTRA, Gjirokastër, Albania KRISANTHI NAKA, UNIVERSITY OF GJIROKASTRA, Gjirokastër, Albania
Full text:	Download Issue 3 [PDF]