Timeline for A ring with 2 minimal left ideal and 3 minimal right ideal
Current License: CC BY-SA 3.0
10 events
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| Sep 29, 2013 at 14:48 | comment | added | Boris Novikov | @Silvi: I don't interested by prime ideals, but I think it is not a difficult problem. As to references, see Okniński, J. Semigroup Algebras. New York: Dekker, 1991. | |
| Sep 29, 2013 at 14:43 | comment | added | user37834 | Thanks. How about prime ideals? Any characterization for them? By the way do you know any references concerning Munn algebra's I and their ideal structure, they seems to be very interesting. | |
| Sep 28, 2013 at 20:19 | comment | added | Boris Novikov | @Silvi: Sorry, I had read your first question wrong mean "minimal" instead "maximal". A maximal ideal is a direct sum of all minimal ideals without one of them. | |
| Sep 28, 2013 at 19:23 | comment | added | user37834 | So what are the maximal left ideals of $M$? | |
| Sep 26, 2013 at 21:05 | comment | added | Boris Novikov | @Silvi: There is an analogy with usual matrix rings over a field: if we consider a minimal left ideal as the additive group, it is the direct sum of the additive groups of the field. | |
| Sep 26, 2013 at 20:48 | comment | added | user37834 | +1 Nice. What can you tell about the form of maximal (left or right) and prime ideals of $M$ (or $M_1$)? | |
| Sep 26, 2013 at 19:55 | history | edited | Boris Novikov | CC BY-SA 3.0 |
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| Sep 26, 2013 at 19:43 | comment | added | Boris Novikov | @Manny Reyes: Thank you very much, I forgot about the identity. I will correct the answer. | |
| Sep 26, 2013 at 19:11 | comment | added | Manny Reyes | This is a very clever idea, but this ring doesn't seem to have an identity element. Such an element $X \in M$ would need to be a $3 \times 2$ matrix satisfying $PX = I_2$ and $XP = I_3$. The latter is impossible by rank considerations. Am I missing something? | |
| Sep 26, 2013 at 16:37 | history | answered | Boris Novikov | CC BY-SA 3.0 |