Atmospheric pressures In weather issues, High Pressure cells are characterized by warmer air (of lower density). Low pressure cells have colder air (higher density). Any literature search on this leads to the basic PV=nRT, describing the opposite of the above descriptors. What's the logic and/or explanation for this atmospheric pressure phenomena?
 A: 
High Pressure cells are characterized by warmer air (of lower density)

I think you're putting a few separate things together.

*

*High pressure is often associated with warmer weather, but not always.  There may be significant temperature differences on both sides of a front, but the pressures may be identical.

*Warmer air will have less density than cooler air when the pressure is the same.

If you compare a low and a high at the same altitude, you can be sure the pressures are different, but you can't speak to the temperature or the density without more information.
Two separated parcels may have different densities (and therefore different number of moles for a fixed volume).  So there is no reason to suppose that PV=nRT does not hold.
A: If you have air in a container and heat it, the temperature will increase and the pressure inside as well. The reason is that the air molecules have larger kinetic energy, they move faster, hitting the walls and each other harder. In other words, the air tends to expand, which is not possible because of the container.
In the atmosphere, hot air can expand, and it does it towards larger altitudes where the density is lower, of course.
So if you heat the ground, like at the equator, it will heat the air close to the ground, which will lift up, therefore leaving a low pressure area. The lifted air rises and cools while lifting until the tropoause (where it cannot rise any further because temperature in the stratosphere is increasing again due to absorption of UV light by ozone). Here you get a high pressure region. The air now moves to the north and south (in the example with the equator) and sinks again at higher latitudes (thereby warming), so that you get a high pressure region at the ground. This is called the hadley cell, which is rather stable.
So the ideal gas law is of course true, but the situation in the atmosphere is more complex than in a container.
A: In the range of pressures we have in the troposphere the gas law holds perfectly, but we have to interprete it in a proper way.  Lest's solve for P the equation of the gas law:
$$P=\frac{n} {V}RT $$
Now, a warm dry air mass have a higher temperature than a cold dry air mass, but the number of moles per unit volume is smaller in the warm mass. So we can not conclude that pressure in a warm air mass has higher or lower pressure than in a cold air mass. In fact there are cold anticyclones, as you can find in Canada in winter, and warm anticyclones, as you can find around Azores Islands in summer. Similarly, there are cold cored lows, like mid-latitude depressions and warm cored lows, like tropical cyclones.
Apart from this, is also important to know how thick is the atmosphere above a given pressure system. Among two columns of air with the same temperature profile the thicker one will weight more and will produce a higher surface pressure. Cold cored systems, like mid-latitude lows, have much smaller thickness than, for example, warm maritime antycyclones, and this have an important impact on system surface pressures.
A further complication arises from humidity content. As water vapor is lighter than air, given two air masses with the same temperature, the drier one will weight more so its pressure will be higher than that of the more moistened mass.
