Timeline for Finite Idempotent Semirings (Dioids)
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2010 at 19:52 | comment | added | user4977 | Sorry. Your previous version was asking how many did not coincide with a max operation. I am saying that all of them do appear as a max with respect to some ordering. | |
| Sep 27, 2010 at 16:53 | comment | added | decomwe | The numbers from 0 to n with the relation 0<1<2<...<n form a total order and the max function on this order is a commutative idempotent operation. | |
| Sep 27, 2010 at 12:42 | comment | added | user4977 | Well if you have a commutative idempotent operation + then the relation $\leq$ defined by $a\leq b$ iff $a+b=b$ is a partial order. This is why (if I am correctly interpreting what you are asking) I think the answer to your second question is zero. | |
| Sep 27, 2010 at 8:50 | history | edited | decomwe | CC BY-SA 2.5 |
rewrite 2nd part
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| Sep 27, 2010 at 8:48 | comment | added | decomwe | Oops. Getting myself muddled. Yes. Thankyou. | |
| Sep 27, 2010 at 2:59 | comment | added | user4977 | Regarding your second question: Do you mean to ask how many have an addition which doesn't come from a max operation? I ask because I am really only familiar with the semiring one gets by using "max" as the addition and "plus" as the multiplication on the reals. However, if this is your intended question, then the answer may be zero. Also, have you looked at any of Golan's texts on semirings? | |
| Sep 26, 2010 at 21:06 | history | edited | decomwe | CC BY-SA 2.5 |
refs and axioms
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| Sep 26, 2010 at 20:48 | comment | added | decomwe | These idempotent semirings without any further restrictions are described as a vast class by M. A. Shubin (1992), "Algebraic remarks on idempotent semirings and the kernel theorem in spaces of bounded functions’" in books.google.com/books?&id=ZoxXoYoZuo0C&oi=fnd&pg=PA151 | |
| Sep 26, 2010 at 20:41 | comment | added | decomwe | Yes to all those. | |
| Sep 26, 2010 at 16:54 | comment | added | Todd Trimble | Do your semirings have a multiplicative identity? So in other words, do you mean the underlying additive structure is a commutative monoid, the underlying multiplicative structure is a monoid, and multiplication distributes over addition? | |
| Sep 26, 2010 at 13:20 | history | asked | decomwe | CC BY-SA 2.5 |