Study on filter soft partially ordered semigroups

doi:10.3785/j.issn.1008-9497.2023.05.001

Journal of Zhejiang University (Science Edition)

2023, Vol. 50

Issue (5): 521-526 DOI: 10.3785/j.issn.1008-9497.2023.05.001

Mathematics and Computer Science

Study on filter soft partially ordered semigroups

Haiqin SHAO(

),Maolin LIANG,Jianwei HE

School of Mathematics and Statistics，Tianshui Normal University，Tianshui 741001，Gansu Province，China

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Abstract

In this paper, we apply the theory of soft sets to partially ordered semigroup. First, several new notions such as left (right) filter soft partially ordered semigroup, filter soft partially ordered semigroup, whole left (right) filter soft partially ordered semigroup, whole filter soft partially ordered semigroup, prime left (right) ideal soft partially ordered semigroup, prime ideal soft partially ordered semigroup over partially ordered semigroups $S$ are introduced. Further, with prime left (right) ideal soft partially ordered semigroup and prime ideal soft partially ordered semigroup over $S$ , the necessary and sufficient conditions that the non-null soft set over $S$ is a right (left) filter soft partially ordered semigroup and filter soft partially ordered semigroup over $S$ are given separately. Finally, quotient ordered homomorphic images and inverse images under partially ordered homomorphic on left (right) filter soft partially ordered semigroup, filter soft partially ordered semigroup, whole left (right) filter soft partially ordered semigroup and whole filter soft partially ordered semigroup are studied,and some related conclusions are obtained.

Key words： partially ordered semigroups filter soft partially ordered semigroups whole filter soft partially ordered semigroups prime ideal soft partially ordered semigroups partially ordered homomorphisms quotient ordered homomorphisms

Received: 08 July 2022 Published: 16 September 2023

CLC:

O152.7

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Cite this article:

Haiqin SHAO,Maolin LIANG,Jianwei HE. Study on filter soft partially ordered semigroups. Journal of Zhejiang University (Science Edition), 2023, 50(5): 521-526.

URL:

https://www.zjujournals.com/sci/EN/Y2023/V50/I5/521

滤子软偏序半群研究

将软集合理论应用于偏序半群。首先，引入偏序半群 $S$ 上的左（右）滤子软偏序半群、滤子软偏序半群、完全左（右）滤子软偏序半群、完全滤子软偏序半群、素左（右）理想软偏序半群和素理想软偏序半群概念。其次，利用素左（右）理想软偏序半群和素理想软偏序半群，分别给出了 $S$ 上的一个非空软集合是右（左）滤子软偏序半群和滤子软偏序半群的充分必要条件。最后，研究了 $S$ 上的左（右）滤子软偏序半群、滤子软偏序半群、完全左（右）滤子软偏序半群和完全滤子软偏序半群的商序同态像和在偏序同态映射下的逆像，得到了一些相关结论。

关键词： 偏序半群, 滤子软偏序半群, 完全滤子软偏序半群, 素理想软偏序半群, 偏序同态, 商序同态

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$b$	$e$	$b$	$e$	$e$	$e$
$c$	$c$	$c$	$c$	$c$	$c$
$d$	$d$	$d$	$d$	$d$	$d$
$e$	$e$	$e$	$e$	$e$	$e$

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$d$	$a$	$d$	$a$	$d$	$d$
$e$	$a$	$d$	$c$	$d$	$e$


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