I feel like that's the same concept, but a different sentence. It's different in English too: "She has good memory" versus "She has A good memory."
The difference is between an abstract entity and a concrete entity.
An easy way to tell the difference (at least in English) is to think about whether there can be more than one of the object. If it could be either singular or plural, it's probably not abstract.
For example, 'your memory' (here meaning your recollection of a past event) is a concrete entity, as evidenced by the fact that you can possess many such memories. (Not to be confused with "concrete noun" in the sense of a physical object!)
But 'your memory' (here meaning your general capacity for remembering things) is an abstract entity, because you only have one such capacity at a given time -- just like you can't have two intelligences, or two ages, or two heights.
Does anyone have further explanation as to why leaving the definite article out is also correct in this example?
We are into abstractions, here. With the article the sentence would be specific. Without the article it becones abstract. And I think this is what we are presently being taught.
Except that the sentence without "una" is translated as "She has a good memory."
'Why not "tienes una buena memoria"?' Answer: because that would mean having a single, specific memory of something whereas we are trying to express a good ability to memorize things, and that we express as "a good memory" in English but we have to drop the "a" in Spanish (not use una) to avoid changing the meaning from having the ability to memorize to just having one memory.
I think because it's the difference between ability to remember (la memoria) and a remembrance of a thing, event, etc. (un recuerdo).
I think that is a good way to put it. That is the difference between an abstraction and something not abstract, something specific.
Before non-count nouns, Spanish doesn't need an "un/a" for "a", even in phrases which the English might need an "a".
"Memory" is a non-count noun, in the context of this specific sentence.
I think this is a simple version of what zeunysos is saying.
If you were talking to a guy would it be "tienes bueno memoria"? Do you switch the buena to bueno?
Buena should match with memoria not with the one you talk with. And memoria is feminine.
Adjective should match the thing you are describing in gender, which in that case is "la memoria' which is feminine. So, the adjective should be feminine too "buena" regardless if you are talking to a woman or a man. Hope this is clear.
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Samples I found show úna is used as commonly as without so either is right -
Tiene una buena amiga en ti. She's got a good friend in you.
Esta docilidad tiene una buena razón. There is a good reason for this docility.
Parece que tiene una buena coartada. It seems he has a good alibi.
Cada ventana tiene una buena vista. A good view from every window.
Mi piel tiene una buena pigmentación. I have a good pigmentation of the skin.
Because they used the "Tu´" verb conjugate which is "Tienes", if it was "I have" they would have used the "Yo" verb conjugate which is "Tengo".