Reputation
1,902
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
Badges
4 13
Newest
 Explainer
Impact
~70k people reached

Mar
31
answered why $(\theta _{1}\circ \theta _{2})^{\vee }\subset(\theta _{2}\circ \theta _{1})^{\vee } $
Mar
30
comment Show Sg$(X) = X\cup E(X) \cup E^{2}(X)\cup …$
Is this homework? If so, perhaps you should tag it as such. Also, what have you tried? Have you given some thought to the question? Do the definitions make sense to you?
Feb
11
comment Algebraic systems
Please see my answer to this question.
Jan
26
answered whether given lattice is distributive or complemented or both?
Jan
22
comment Which texts do you recommend to study universal algebra and lattice theory?
@KevinCarlson Lattices are usually studied alongside universal algebra because of the fundamental role they play. Besides the examples Alex mentions, there's the lattice of varieties or equational theories. So, while it's true that lattices are "a particular case of universal algebras," they play a more central role than algebras of other types.
Jan
22
revised Example of a map between two lattices such that the map is an order embedding but not a lattice embedding
fixed title to match actual question
Jan
22
revised Example of a map between two lattices such that the map is an order embedding but not a lattice embedding
edited body
Jan
22
suggested approved edit on Example of a map between two lattices such that the map is an order embedding but not a lattice embedding
Jan
22
answered Example of a map between two lattices such that the map is an order embedding but not a lattice embedding
Nov
6
revised Which texts do you recommend to study universal algebra and lattice theory?
deleted 116 characters in body
Oct
28
revised Which texts do you recommend to study universal algebra and lattice theory?
deleted 1 character in body
Oct
28
answered Which texts do you recommend to study universal algebra and lattice theory?
Oct
19
comment Lists of small lattices and posets
Peter Jipsen maintains some lists of small ordered algebraic structures, including a nice page/applet that generates Hasse diagrams of all finite lattices with at most 7 elements here. (Some of the links on that page seem to be broken right now. I emailed Peter to let him know. Hopefully they will be fixed soon.) There are also diagrams of all connected posets of size 4 and 5 here.
Oct
19
revised Lists of small lattices and posets
the title seemed only marginally related to the question
Oct
19
suggested approved edit on Lists of small lattices and posets
Sep
30
awarded  Explainer
Sep
27
comment Lattice which is not bounded lattice
The set $(0,1) \subset \mathbb{R}$ with the usual $\leq$ order is another example. It is not bounded below (above) because there is no element in $(0,1)$ that is less (greater) than every other element.
Sep
22
comment A Course in Universal Algebra (Millennium edition), page 74
@TimLee No, the "Sub" tab draws the lattice of subalgebras of the currently selected algebra. If "Sub" showed a 2x2, that means you're still looking at the 2-element lattice. After following the steps I gave above, you will see two lines in the Algebras list at the bottom of the UACalc window. The first is lat2. The second is the free algebra over lat2 that you constructed using the Tasks menu. Now, from this list of Algebras, select "F(2) over lat2". You can then click the Edit tab and see what the multiplication table is for the free algebra, and draw it using Drawing-->Algebra.
Sep
20
answered What does a lattice of the direct power of the two-element chain look like?
Sep
19
comment A Course in Universal Algebra (Millennium edition), page 74
You may find it instructive to try out some small examples in the Universal Algebra Calculator (www.uacalc.org). After you launch the application, try, for example: File -> Built In Algs -> lat2. Then: Tasks -> Free Algebra. You will be prompted for the number if generators. Enter 2, then click "Drawing" and "Go". You will see a 2x2 lattice. When learning this stuff, UACalc can be useful for verifying pencil/paper calculations.