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Zero-Divisor Graphs of Some Algebraic Structures

by Avinash Patil
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Current price ₹7,715.00
Original price ₹8,794.00
Original price ₹8,794.00
Original price ₹8,794.00
(-12%)
₹7,715.00
Current price ₹7,715.00

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Book cover type: Paperback
  • ISBN13: 9786209231346
  • Binding: Paperback
  • Subject: N/A
  • Publisher: LAP Lambert Academic Publishing
  • Publisher Imprint: LAP Lambert Academic Publishing
  • Publication Date:
  • Pages: 184
  • Original Price: GBP 69.51
  • Language: English
  • Edition: N/A
  • Item Weight: 254 grams
  • BISAC Subject(s): General

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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