TY - JOUR
T1 - On essential elements in a lattice and Goldie analogue theorem
AU - Sahoo, Tapatee
AU - Kedukodi, Babushri Srinivas
AU - Shum, Kar Ping
AU - Panackal, Harikrishnan
AU - Kuncham, Syam Prasad
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - We introduce the concept of essentiality in a lattice L with respect to an element δ ∈ L. We define notions such as δ-essential, δ-uniform elements and obtain some of their properties. Examples of lattices are given wherein essentiality can be retained with respect to an arbitrary element (specifically, there are elements in L which are δ-essential but not essential). We prove Goldie analogue results in terms of δ-uniform elements and δ-v-independent sets. Furthermore, we define a graph with respect to δ-essential element in a lattice and study its properties.
AB - We introduce the concept of essentiality in a lattice L with respect to an element δ ∈ L. We define notions such as δ-essential, δ-uniform elements and obtain some of their properties. Examples of lattices are given wherein essentiality can be retained with respect to an arbitrary element (specifically, there are elements in L which are δ-essential but not essential). We prove Goldie analogue results in terms of δ-uniform elements and δ-v-independent sets. Furthermore, we define a graph with respect to δ-essential element in a lattice and study its properties.
UR - http://www.scopus.com/inward/record.url?scp=85110635078&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85110635078&partnerID=8YFLogxK
U2 - 10.1142/S1793557122500917
DO - 10.1142/S1793557122500917
M3 - Article
AN - SCOPUS:85110635078
SN - 1793-5571
VL - 15
JO - Asian-European Journal of Mathematics
JF - Asian-European Journal of Mathematics
IS - 5
M1 - 2250091
ER -