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What kind of algebra-like structure is Interval Arithmetic (properties are defined in chapter 4)?

Basically, interval addition and multiplication are both commutative and associative. Additive and multiplicative identity elements exist. But, the inverse elements for addition and multiplication don't exist and distributivity doesn't hold. Although, subdistributivity holds.

Moore, Ramon E.; Kearfott, R. Baker; Cloud, Michael J., Introduction to interval analysis, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-69-6/pbk; 978-0-89871-771-6/ebook). xi, 223 p. (2009). ZBL1168.65002.

Eric Wofsey
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Denis Mazzucato
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  • See also https://math.stackexchange.com/questions/4119610/is-interval-arithmetic-an-integral-domain – lhf Jun 24 '21 at 16:59
  • Thanks for the reference, I would say that Interval Arithmetic is then a (subdistributivity) commutative monoid. – Denis Mazzucato Jun 25 '21 at 09:55

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