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Zero-Divisor Graphs of Some Algebraic Structures

By Avinash Patil

Zero-Divisor Graphs of Some Algebraic Structures

By Avinash Patil

0 - Default Title
Description
This book studies a graph assigned to the zero divisors of a ring with involution *, which is an anti-homomorphism of order two. The *-rings with zero-divisor graph connected are characterized and results about chromatic number, clique number, girth are obtained. An equivalent condition for adjacency in the zero-divisor graph of Rickart *-rings is obtained using the right projections. The zero-divisors graphs of Rickart *-rings are thoroughly investigated using the prime strict spectrum. Also, the zero-divisor graphs of dismantlable lattices are examined and are used to obtain the zero-divisor graphs of Rickart *-rings. The zero-divisor graphs of dismantlable lattices are characterized using the comparability graphs and non-ancestor graphs. For two lower dismantlable lattices, it is proved that their zero-divisor graphs are isomorphic if and only if the lattices are isomorphic. At last, the orthogonality graphs of ortho lattices are investigated and their connection with zero-divisor graphs is established.
Product details
Binding:
Paperback
Number of Pages:
184
Release Date:
2025-11-26
Publication Date:
2025-11-26
Publisher:
LAP LAMBERT Academic Publishing
Languages:
Original: English
ISBN10:
6209231349
ISBN13:
9786209231346
Weight:
292 g
Height:
150 cm
Width:
220 cm
Thickness:
12 cm
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