Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • A commutativity theorem for power-associative rings

  • D. L. Outcalt, Adil Yaqub
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 3 / Issue 1 / August 1970
    Published online by Cambridge University Press:
    17 April 2009, pp. 75-79
    Print publication:
    August 1970
    • Article
      • You have access
    • PDF
    • Export citation

  • Let R be a power-associative ring with identity and let I be an ideal of R such that R/I is a finite field and x ≡ y (mod I) implies x2 = y2 or both x and y commute with all elements of I. It is proven that R must then be commutative. Examples are given to show that R need not be commutative if various parts of the hypothesis are dropped or if “x2 = y2” is replaced by “xk = yk” for any integer k > 2.

  • An Extension of the Class of Alternative Rings

  • D. L. Outcalt
  • Journal:
    Canadian Journal of Mathematics / Volume 17 / 1965
    Published online by Cambridge University Press:
    20 November 2018, pp. 130-141
    Print publication:
    1965
    • Article
      • You have access
    • PDF
    • Export citation

  • Define R to be a ring of characteristic not 2 or 3 satisfying the identity

    (1)       (x,y,z) = (y,z,x)

    for all x, y, z ∊ R, where by characteristic not p is meant x —> px is a one-toone mapping of R upon R. The associator (a, b, c) of R is defined by (a, b, c) = ab·c — a·bc. lf R also satisfies the identity

    (2)     (x, x, x) = 0