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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Zero-Divisor Graphs of Some Algebraic Structures

Zero-Divisor Graphs of Some Algebraic Structures

Patil, Avinash

Paperback

General Mathematics

ISBN10: 6209231349
ISBN13: 9786209231346
Publisher: LAP Lambert Academic Publishing
Published: Nov 26 2025
Pages: 184
Weight: 0.56
Height: 0.42 Width: 6.00 Depth: 9.00
Language: English
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.

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