I don't have gymnastic rings or a pull up bar, what other alternatives do I have?

Replace pull up bar or rings with these exercises.

If you have a portable pull up bar that goes between the door, you can set it low and do inverted rows with it. There can also be places to do inverted rows anywhere in the house: under stairways or behind a table (grip the edge). 

You can also use a band as demonstrated in the video. 

All rows can also be replaced with a dumbbell, a kettlebell or even water bottles. The weight should be relatively light and easy to control.

Dumbbell row: take a bent over position and pull the weight next to your body while keeping the hips and core stable. 

Rear delt row: as seen in the picture above. Otherwise the same except you pull more horizontally to the side similar to the bulgarian row. Can be done with one or two weights.

Facepull row: pull close to your head as seen in the picture below. Can be done with one or two dumbbells. A big water pull is very good for this exercise as well. You can lean against a wall for added stability.

You can also do  bodyweight air rows with zero equipment. It may look easy but it's very effective when done right. The exercise looks like this:

Similar to other rows, you keep the hips and core stable. Pull your shoulder blades and arms behind with control, hold it there and lower with control. Bulgarian rows and facepulls can also be replaced with this exercise with small modifications (with the facepull you pull next to your head).

Also, gymnastic rings are worth the investment. They are an excellent tool and can be as inexpensive as $30 USD and you can hang them on your pull up bar. Most fitness stores should have them.